Research Group of Prof. Dr. D. Peterseim
Institute for Numerical Simulation
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Publications of Group Peterseim

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Submitted Articles:

[1] D. Gallistl and D. Peterseim. Numerical stochastic homogenization by quasi-local effective diffusion tensors. 2017. INS Preprint No. 1701.
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[2] R. Kornhuber, D. Peterseim, and H. Yserentant. An analysis of a class of variational multiscale methods based on subspace decomposition. November 2016. Submitted for publication.
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[3] D. Brown and D. Gallistl. Multiscale sub-grid correction method for time-harmonic high-frequency elastodynamics with wavenumber explicit bounds. 2016. INS Preprint No. 1620.
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[4] D. Gallistl and D. Peterseim. Computation of local and quasi-local effective diffusion tensors in elliptic homogenization. 2016. INS Preprint No. 1619.
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[5] P. Henning and D. Peterseim. Crank-Nicolson Galerkin approximations to nonlinear Schrödinger equations with disorder potentials. 2016. INS Preprint No. 1621.
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[6] G. Li, D. Peterseim, and M. Schedensack. Error analysis of a variational multiscale stabilization for convection-dominated diffusion equations in 2d. ArXiv e-prints, 2016. Also available as INS Preprint No. 1612.
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Journal Papers:

[1] D. Gallistl. Variational formulation and numerical analysis of linear elliptic equations in nondivergence form with Cordes coefficients. Siam J. Numer. Anal., 2017. Accepted for publication.
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[2] D. Gallistl, P. Huber, and D. Peterseim. On the stability of the Rayleigh-Ritz method for eigenvalues. 2017. Accepted for publication in Numerische Mathematik. Available as INS Preprint No. 1527.
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[3] P. Hennig, M. Kästner, P. Morgenstern, and D. Peterseim. Adaptive Mesh Refinement Strategies in Isogeometric Analysis - A Computational Comparison. Comp. Meth. Appl. Mech. Eng., 316:424–-448, 2017.
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[4] A. Målqvist and D. Peterseim. Generalized finite element methods for quadratic eigenvalue problems. ESAIM Math. Model. Numer. Anal., 51(1):147-163, 2017.
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[5] D. Peterseim. Eliminating the pollution effect in Helmholtz problems by local subscale correction. Math. Comp., 86:1005-1036, 2017.
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[6] D. Peterseim and M. Schedensack. Relaxing the CFL condition for the wave equation on adaptive meshes. J. Sci. Comput., 2017. Online First.
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[7] M. Schedensack. Mixed finite element methods for linear elasticity and the Stokes equations based on the Helmholtz decomposition. ESAIM Math. Model. Numer. Anal., 51(2):399-425, 2017.
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[8] M. Schedensack. A new generalization of the P1 non-conforming FEM to higher polynomial degrees. Comput. Methods Appl. Math., 17(1):161-185, 2017. also available as INS Preprint No. 1507 and arXiv e-print 1505.02044.
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[9] P. Morgenstern. Globally structured three-dimensional analysis-suitable T-splines: Definition, linear independence and $m$-graded local refinement. SIAM J. Numer. Anal., 54(4):2163-2186, May 2016. Also available as INS Preprint No. 1508.
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[10] M. Schedensack. A new discretization for mth-Laplace equations with arbitrary polynomial degrees. SIAM J. Numer. Anal., 54(4):2138-2162, 2016. Also available as INS Preprint No. 1528 and arXiv e-print 1512.06513.
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[11] D. Boffi, D. Gallistl, F. Gardini, and L. Gastaldi. Optimal convergence of adaptive FEM for eigenvalue clusters in mixed form. Math. Comp., 2016. Accepted for publication.
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[12] D. Brown and D. Peterseim. A multiscale method for porous microstructures. SIAM MMS, 14:1123-1152, 2016.
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[13] D. L. Brown and V. Taralova. A multiscale finite element method for Neumann problems in porous microstructures. Disc. and Cont. Dyn. Sys., 2016. In press. Also available as INS Preprint No. 1503.
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[14] D. L. Brown and M. Vasilyeva. A generalized multiscale finite element method for poroelasticity problems I: Linear problems. Journal of Computational and Applied Mathematics, 294(C):372-388, 2016. Also available as INS Preprint No. 1516.
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[15] A. Buffa, C. Giannelli, P. Morgenstern, and D. Peterseim. Complexity of hierarchical refinement for a class of admissible mesh configurations. Computer Aided Geometric Design, 47:83-92, 2016.
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[16] C. Carstensen, D. Gallistl, and M. Schedensack. L2 best-approximation of the elastic stress in the Arnold-Winther FEM. IMA J. Numer. Anal., 36(3):1096-1119, 2016.
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[17] C. Carstensen, B. Reddy, and M. Schedensack. A natural nonconforming FEM for the Bingham flow problem is quasi-optimal. Numer. Math., 133(1):37-66, 2016.
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[18] D. Gallistl. Stable splitting of polyharmonic operators by generalized Stokes systems. Math. Comp., 2016. Accepted for publication. Also available INS Preprint No. 1529.
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[19] C. Kreuzer and M. Schedensack. Instance optimal Crouzeix-Raviart adaptive finite element methods for the Poisson and Stokes problems. IMA J. Numer. Anal., 36(2):593-617, 2016.
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[20] D. Peterseim and R. Scheichl. Robust numerical upscaling of elliptic multiscale problems at high contrast. Computational Methods in Applied Mathematics, 16:579-603, 2016.
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[21] D. Gallistl and D. Peterseim. Stable multiscale Petrov-Galerkin finite element method for high frequency acoustic scattering. Comp. Meth. Appl. Mech. Eng., 295:1-17, 2015.
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[22] D. L. Brown, Y. Efendiev, G. Li, and V. Savatorova. Homogenization of high-contrast brinkman flows. SIAM MMS, 13(2):472-490, 2015.
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[23] C. Carstensen, D. Gallistl, and J. Gedicke. Justification of the saturation assumption. Numer. Math., 2015. Published online.
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[24] C. Carstensen, D. Gallistl, and N. Nataraj. Comparison results of nonstandard P2 finite element methods for the biharmonic problem. ESAIM Math. Model. Numer. Anal., 49:977-990, 2015.
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[25] C. Carstensen, D. Gallistl, and M. Schedensack. Adaptive nonconforming Crouzeix-Raviart FEM for eigenvalue problems. Math. Comp., 84(293):1061-1087, 2015.
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[26] C. Carstensen, K. Köhler, D. Peterseim, and M. Schedensack. Comparison results for the Stokes equations. Appl. Numer. Math., 95:118-129, 2015.
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[27] C. Carstensen, D. Peterseim, and A. Schröder. The norm of a discretized gradient in H(div)* for a posteriori finite element error analysis. Numer. Math., 132(3):519-539, 2015.
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[28] C. Carstensen and M. Schedensack. Medius analysis and comparison results for first-order finite element methods in linear elasticity. IMA J. Numer. Anal., 35(4):1591-1621, 2015.
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[29] M. Eigel and D. Peterseim. Simulation of composite materials by a network fem with error control. Computational Methods in Applied Mathematics (online), 15(1):21-37, 2015.
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[30] D. Gallistl. An optimal adaptive FEM for eigenvalue clusters. Numer. Math., 130(3):467-496, 2015.
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[31] D. Gallistl. Morley finite element method for the eigenvalues of the biharmonic operator. IMA J. Numer. Anal., 35(4):1779-1811, 2015.
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[32] P. Morgenstern and D. Peterseim. Analysis-suitable adaptive T-mesh refinement with linear complexity. Computer Aided Geometric Design, 34:50-66, 2015. Also available as INS Preprint No. 1409.
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[33] P. Vignal, L. Dalcin, D. L. Brown, N. Collier, and V. M. Calo. An energy-stable convex splitting for the phase-field crystal equation. 2015. accepted for publication in Computers and Structures.
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[34] C. Carstensen and D. Gallistl. Guaranteed lower eigenvalue bounds for the biharmonic equation. Numer. Math., 126(1):33-51, 2014.
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[35] C. Carstensen, D. Gallistl, and J. Hu. A discrete Helmholtz decomposition with Morley finite element functions and the optimality of adaptive finite element schemes. Comput. Math. Appl., 68(12):2167-2181, 2014.
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[36] C. Carstensen, D. Gallistl, F. Hellwig, and L. Weggler. Low-order dPG-FEM for an elliptic PDE. Comput. Math. Appl., 68(11):1503-1512, 2014.
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[37] D. Gallistl. Adaptive nonconforming finite element approximation of eigenvalue clusters. Comput. Methods Appl. Math., 14(4):509-535, 2014.
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[38] D. Gallistl, M. Schedensack, and R. P. Stevenson. A remark on newest vertex bisection in any space dimension. Comput. Methods Appl. Math., 14(3):317-320, 2014.
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[39] P. Henning, A. Målqvist, and D. Peterseim. A localized orthogonal decomposition method for semi-linear elliptic problems. ESAIM: Math. Model. Numer. Anal., 48(05):1331-1349, 2014.
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[40] P. Henning, A. Målqvist, and D. Peterseim. Two-level discretization techniques for ground state computations of bose-einstein condensates. SIAM J. Numer. Anal., 52(4):1525-1550, 2014.
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[41] A. Målqvist and D. Peterseim. Computation of eigenvalues by numerical upscaling. Numer. Math., 130(2):337-361, 2014.
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[42] A. Målqvist and D. Peterseim. Localization of elliptic multiscale problems. Math. Comp., 83(290):2583-2603, 2014.
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[43] D. Peterseim. Composite finite elements for elliptic interface problems. Math. Comp., 83(290):2657-2674, 2014.
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[44] C. Carstensen, D. Gallistl, and M. Schedensack. Discrete reliability for Crouzeix-Raviart FEMs. SIAM J. Numer. Anal., 51(5):2935-2955, 2013.
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[45] C. Carstensen, D. Gallistl, and M. Schedensack. Quasi-optimal adaptive pseudostress approximation of the Stokes equations. SIAM J. Numer. Anal., 51(3):1715-1734, 2013.
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[46] C. Carstensen, D. Gallistl, and J. Hu. A posteriori error estimates for nonconforming finite element methods for fourth-order problems on rectangles. Numer. Math., 124(2):309-335, 2013.
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[47] C. Carstensen, D. Peterseim, and H. Rabus. Optimal adaptive nonconforming FEM for the Stokes problem. Numer. Math., 123(2):291-308, 2013.
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[48] D. Elfverson, E. H. Georgoulis, A. Målqvist, and D. Peterseim. Convergence of a discontinuous galerkin multiscale method. SIAM J. Numer. Anal., 51(6):3351-3372, 2013.
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[49] P. Henning and D. Peterseim. Oversampling for the multiscale finite element method. Multiscale Model. Simul., 11(4):1149-1175, 2013.
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[50] D. Peterseim and C. Carstensen. Finite element network approximation of conductivity in particle composites. Numer. Math., 124(1):73-97, 2013.
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[51] C. Carstensen, D. Peterseim, and M. Schedensack. Comparison results of finite element methods for the Poisson model problem. SIAM J. Numer. Anal., 50(6):2803-2823, 2012.
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[52] D. Peterseim. Robustness of Finite Element Simulations in Densely Packed Random Particle Composites. Netw. Heterog. Media, 7(1), 2012.
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[53] D. Peterseim and S. Sauter. Finite Elements for Elliptic Problems with Highly Varying, Nonperiodic Diffusion Matrix. Multiscale Model. Simul., 10(3):665-695, 2012.
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[54] L. Banjai and D. Peterseim. Parallel multistep methods for linear evolution problems. IMA J. Numer. Anal., 32(3):1217-1240, 2011.
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[55] D. Peterseim and S. A. Sauter. Finite element methods for the Stokes problem on complicated domains. Comp. Meth. Appl. Mech. Eng., 200(33-36):2611-2623, 2011.
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[56] D. Peterseim and S. A. Sauter. The composite mini element - coarse mesh computation of Stokes flows on complicated domains. SIAM J. Numer. Anal., 46(6):3181-3206, 2008.
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Refereed Articles in Collections:

[1] D. Peterseim. Variational multiscale stabilization and the exponential decay of fine-scale correctors. In G. R. Barrenechea, F. Brezzi, A. Cangiani, and E. H. Georgoulis, editors, Building Bridges: Connections and Challenges in Modern Approaches to Numerical Partial Differential Equations, volume 114 of Lecture Notes in Computational Science and Engineering. Springer, May 2016. Also available as INS Preprint No. 1509.
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[2] S. Brenner, M. Oh, S. Pollock, K. Porwal, M. Schedensack, and N. Sharma. A C0 interior penalty method for elliptic optimal control problems with pointwise state constraints in three dimensions. In S. Brenner, editor, Topics in Numerical Partial Differential Equations and Scientific Computing, volume 160 of The IMA Volumes in Mathematics and its Applications. Springer, 2016. To appear.
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[3] D. Brown, D. Gallistl, and D. Peterseim. Multiscale Petrov-Galerkin method for high-frequency heterogeneous Helmholtz equations. In M. Griebel and M. A. Schweitzer, editors, Meshfree Methods for Partial Differential Equations VII, Lecture Notes in Computational Science and Engineering. 2016. Accepted for publication. Also available as INS Preprint No. 1526.
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[4] C. Carstensen, D. Gallistl, and B. Krämer. Numerical algorithms for the simulation of finite plasticity with microstructures. In S. Conti and K. Hackl, editors, Analysis and computation of microstructure in finite plasticity, volume 78 of Lecture Notes in Applied and Computational Mechanics, pages 1-30. Springer, 2015.
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[5] P. Henning, P. Morgenstern, and D. Peterseim. Multiscale partition of unity. In M. Griebel and M. A. Schweitzer, editors, Meshfree Methods for Partial Differential Equations VII, volume 100 of Lecture Notes in Computational Science and Engineering, pages 185-204. Springer International Publishing, 2015.
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Edited Proceedings:

[1] C. Carstensen, B. Engquist, and D. Peterseim. Computational Multiscale Methods. 2015.
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Articles in Proceedings:

[1] P. Bringmann, C. Carstensen, D. Gallistl, F. Hellwig, D. Peterseim, S. Puttkammer, H. Rabus, and J. Storn. Towards adaptive discontinuous petrov-galerkin methods. PAMM, 16(1):741-742, 2016.
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[2] D. Gallistl, D. Peterseim, and C. Carstensen. Multiscale petrov-galerkin fem for acoustic scattering. PAMM, 16(1):745-746, 2016.
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[3] D. Peterseim and M. Schedensack. Relaxing the CFL condition for the wave equation on adaptive meshes. PAMM, 16(1):765-766, 2016.
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[4] D. Gallistl and D. Peterseim. Multiscale Petrov-Galerkin finite element method for high frequency acoustic scattering. Oberwolfach Reports, 12(3):2580-2581, 2015.
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[5] M. Schedensack. A class of mixed finite element methods based on the helmholtz decomposition. Oberwolfach Rep., 12(3):2555-2556, 2015.
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[6] P. Henning, A. Målqvist, and D. Peterseim. Two-level discretization for the Gross-Pitaevskii eigenvalue problem with a rough potential. to appear in Oberwolfach Rep., 2014.
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[7] A. Målqvist and D. Peterseim. Multiscale techniques for solving quadratic eigenvalue problems. to appear in Oberwolfach Rep., 2014.
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[8] D. Gallistl. An optimal adaptive FEM for eigenvalue clusters. Oberwolfach Reports, 10(4):3267-3270, 2013.
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[9] A. Målqvist and D. Peterseim. Numerical upscaling of eigenvalue problems. Oberwolfach Rep., 10(1):402-405, 2013.
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[10] D. Peterseim and A. Målqvist. Spectrum-preserving two-scale decompositions with applications to numerical homogenization and eigensolvers. Oberwolfach Rep., 10(1):850-853, 2013.
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[11] M. Schedensack, C. Carstensen, and D. Gallistl. Adaptive nonconforming Crouzeix-Raviart FEM for eigenvalue problems. Oberwolfach Rep., 10(4):3270-3272, 2013.
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[12] D. Gallistl, C. Carstensen, and M. Schedensack. Quasi optimal adaptive pseudostress approximation of the Stokes equations. Oberwolfach Reports, 9(1):497-499, 2012.
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[13] A. Målqvist and D. Peterseim. Finite element discretization of multiscale elliptic problems. Oberwolfach Rep., 9(1):516-519, 2012.
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[14] D. Peterseim, C. Carstensen, and M. Schedensack. Comparison of finite element methods for the Poisson model problem. Oberwolfach Rep., 9(1):584-587, 2012.
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[15] M. Schedensack, C. Carstensen, and D. Peterseim. Comparison results for first-order FEMs. Oberwolfach Rep., 9(1):495-497, 2012.
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[16] D. Peterseim. Triangulating a system of disks. Proc. 26th European Workshop on Computational Geometry (EWCG), pages 241-244, 2010.
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[17] D. Peterseim. Composite finite elements for elliptic interface problems. PAMM, 10(1):661-664, 2010.
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[18] D. Peterseim. Finite element analysis of particle-reinforced composites. Oberwolfach Rep., 6(2):1597-1665, 2009.
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[19] D. Peterseim and S. A. Sauter. Recent advances in composite finite elements. Oberwolfach Rep., 5(2):1233-1293, 2008.
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[20] D. Peterseim and S. A. Sauter. The composite mini element: a new mixed FEM for the Stokes equations on complicated domains. PAMM, 7(1):2020101-2020102, 2007.
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Theses:

[1] P. Morgenstern. Mesh Refinement Strategies for the Adaptive Isogeometric Method. PhD thesis, Institut für Numerische Simulation, Rheinische Friedrich-Wilhelms-Universität Bonn, 2017.
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[2] D. Peterseim. Computational Multiscale Methods for Partial Differential Equations. Habilitation thesis, Humboldt-Universität zu Berlin, 2016.
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[3] M. Schedensack. A class of mixed finite element methods based on the Helmholtz decomposition in computational mechanics. Doctoral dissertation, Humboldt-Universität zu Berlin, Mathematisch-Naturwissenschaftliche Fakultät, 2015.
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[4] D. Gallistl. Adaptive finite element computation of eigenvalues. Doctoral dissertation, Humboldt-Universität zu Berlin, Mathematisch-Naturwissenschaftliche Fakultät II, 2014.
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[5] P. Morgenstern. Lokale Verfeinerung regulärer Triangulierungen in Vierecke. Master's thesis, Institut für Mathematik, Humboldt-Universität zu Berlin, 2013.
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[6] D. Peterseim. The Composite Mini Element: A mixed FEM for the Stokes equations on complicated domains. PhD thesis, Universität Zürich, 2007.
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[7] D. Peterseim. Numerische Analyse parameterabhängiger periodischer Orbits nichtlinearer dynamischer Systeme mittels Mehrzielmethode und effizienter Fortsetzungstechniken. Master's thesis, IfMath, TU Ilmenau, 2004.
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Other Reports:

[1] C. Engwer, P. Henning, A. Målqvist, and D. Peterseim. Efficient implementation of the Localized Orthogonal Decomposition method. ArXiv e-prints, Feb. 2016.
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[2] D. Peterseim. Generalized delaunay partitions and composite material modeling. Matheon Preprint, 690, 2010.
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