Publikationen

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Preprints

[9] Sören Bartels and Marijo Milicevic. Alternating direction method of multipliers with variable step sizes. 2017. [ bib | .pdf ]
[8] Sören Bartels and Patrick Schön. Adaptive approximation of the Monge-Kantorovich problem via primal-dual gap estimates. 2016. [ bib | .pdf ]
[7] Sören Bartels, Philipp Reiter, and Johannes Riege. A simple scheme for the approximation of self-avoiding inextensible curves. 2016. [ bib | .pdf ]
[6] Sören Bartels and Marijo Milicevic. Iterative solution of a constrained total variation regularized model problem. 2016. [ bib | .pdf ]
[5] Sören Bartels. Numerical solution of a Foppl-von Karman model. 2016. [ bib | .pdf ]
[4] Sören Bartels and Marijo Milicevic. Stability and experimental comparison of prototypical iterative schemes for total variation regularized problems. CMAM (accepted), 2015. [ bib | .pdf ]
[3] Sören Bartels. Numerical solution of nonsmooth problems. Lecture notes of a course given at the SAMM 2015, 2015. [ bib | .pdf ]
[2] Sören Bartels, Andrea Bonito, and Ricardo H. Nochetto. Bilayer plates: model reduction, gamma-convergent finite element approximation, and discrete gradient flow. Comm. Pure Appl. Math. (accepted), 2015. [ bib | .pdf ]
[1] Sören Bartels. A simple scheme for the approximation of elastic vibrations of inextensible curves. IMA J. Numer. Anal. (accepted), 2014. [ bib | .pdf ]

Zeitschriftenartikel

[60] Sören Bartels. Broken Sobolev space iteration for total variation regularized minimization problems. IMA J. Numer. Anal., 36(2):493--502, 2016. [ bib | DOI | http | .pdf ]
[59] Sören Bartels. Projection-free approximation of geometrically constrained partial differential equations. Math. Comp., 85(299):1033--1049, 2016. [ bib | DOI | http | .pdf ]
[58] Sören Bartels, Ricardo H. Nochetto, and Abner J. Salgado. A total variation diminishing interpolation operator and applications. Math. Comp., 84(296):2569--2587, 2015. [ bib | DOI | http | .pdf ]
[57] Sören Bartels. Fast and accurate finite element approximation of wave maps into spheres. ESAIM Math. Model. Numer. Anal., 49(2):551--558, 2015. [ bib | DOI | http | .pdf ]
[56] Sören Bartels. Robustness of error estimates for phase field models at a class of topological changes. Comput. Methods Appl. Mech. Engrg., 288:75--82, 2015. [ bib | DOI | http | .pdf ]
[55] Sören Bartels and Peter Hornung. Bending paper and the Möbius strip. J. Elasticity, 119(1-2):113--136, 2015. [ bib | DOI | http | .txt ]
[54] Sören Bartels. Error control and adaptivity for a variational model problem defined on functions of bounded variation. Math. Comp., 84(293):1217--1240, 2015. [ bib | DOI | http | .pdf ]
[53] Sören Bartels, Mario Bebendorf, and Michael Bratsch. A fast and accurate numerical method for the computation of unstable micromagnetic configurations. In Singular phenomena and scaling in mathematical models, pages 413--434. Springer, Cham, 2014. [ bib | DOI | http | .pdf ]
[52] Sören Bartels and Alexander Raisch. Simulation of Q-tensor fields with constant orientational order parameter in the theory of uniaxial nematic liquid crystals. In Singular phenomena and scaling in mathematical models, pages 383--412. Springer, Cham, 2014. [ bib | DOI | http | .pdf ]
[51] Sören Bartels. Quasi-optimal error estimates for implicit discretizations of rate-independent evolutions. SIAM J. Numer. Anal., 52(2):708--716, 2014. [ bib | DOI | http | .pdf ]
[50] Sören Bartels, Ricardo H. Nochetto, and Abner J. Salgado. Discrete total variation flows without regularization. SIAM J. Numer. Anal., 52(1):363--385, 2014. [ bib | DOI | http | .pdf ]
[49] Sören Bartels. A simple scheme for the approximation of the elastic flow of inextensible curves. IMA J. Numer. Anal., 33(4):1115--1125, 2013. [ bib | DOI | http | .pdf ]
[48] Sören Bartels and Tomáš Roubíček. Numerical approaches to thermally coupled perfect plasticity. Numer. Methods Partial Differential Equations, 29(6):1837--1863, 2013. [ bib | .pdf ]
[47] Sören Bartels. Finite element approximation of large bending isometries. Numer. Math., 124(3):415--440, 2013. [ bib | DOI | http | .pdf ]
[46] Sören Bartels. Approximation of large bending isometries with discrete Kirchhoff triangles. SIAM J. Numer. Anal., 51(1):516--525, 2013. [ bib | DOI | http | .pdf ]
[45] Sören Bartels. Total variation minimization with finite elements: convergence and iterative solution. SIAM J. Numer. Anal., 50(3):1162--1180, 2012. [ bib | DOI | http | .pdf ]
[44] Sören Bartels and Patrick Schreier. Local coarsening of simplicial finite element meshes generated by bisections. BIT, 52(3):559--569, 2012. [ bib | DOI | http | .pdf ]
[43] Sören Bartels, Georg Dolzmann, Ricardo H. Nochetto, and Alexander Raisch. Finite element methods for director fields on flexible surfaces. Interfaces Free Bound., 14(2):231--272, 2012. [ bib | DOI | http | .pdf ]
[42] Sören Bartels, Alexander Mielke, and Tomáš Roubíček. Quasi-static small-strain plasticity in the limit of vanishing hardening and its numerical approximation. SIAM J. Numer. Anal., 50(2):951--976, 2012. [ bib | DOI | http | .pdf ]
[41] Sören Bartels and Martin Kružík. An efficient approach to the numerical solution of rate-independent problems with nonconvex energies. Multiscale Model. Simul., 9(3):1276--1300, 2011. [ bib | DOI | http | .pdf ]
[40] Sören Bartels and Rüdiger Müller. Error control for the approximation of Allen-Cahn and Cahn-Hilliard equations with a logarithmic potential. Numer. Math., 119(3):409--435, 2011. [ bib | DOI | http | .pdf ]
[39] Sören Bartels and Tomáš Roubíček. Thermo-visco-elasticity with rate-independent plasticity in isotropic materials undergoing thermal expansion. ESAIM Math. Model. Numer. Anal., 45(3):477--504, 2011. [ bib | DOI | http | .pdf ]
[38] Sören Bartels and Rüdiger Müller. Quasi-optimal and robust a posteriori error estimates in L(L2) for the approximation of Allen-Cahn equations past singularities. Math. Comp., 80(274):761--780, 2011. [ bib | DOI | http | .pdf ]
[37] Sören Bartels, Rüdiger Müller, and Christoph Ortner. Robust a priori and a posteriori error analysis for the approximation of Allen-Cahn and Ginzburg-Landau equations past topological changes. SIAM J. Numer. Anal., 49(1):110--134, 2011. [ bib | DOI | http | .pdf ]
[36] Sören Bartels. Numerical analysis of a finite element scheme for the approximation of harmonic maps into surfaces. Math. Comp., 79(271):1263--1301, 2010. [ bib | DOI | http | .pdf ]
[35] Sören Bartels, Georg Dolzmann, and Ricardo H. Nochetto. A finite element scheme for the evolution of orientation order in fluid membranes. M2AN Math. Model. Numer. Anal., 44(1):1--31, 2010. [ bib | DOI | http | .pdf ]
[34] Sören Bartels and Rüdiger Müller. A posteriori error controlled local resolution of evolving interfaces for generalized Cahn-Hilliard equations. Interfaces Free Bound., 12(1):45--73, 2010. [ bib | DOI | http | .pdf ]
[33] Sören Bartels, Max Jensen, and Rüdiger Müller. Discontinuous Galerkin finite element convergence for incompressible miscible displacement problems of low regularity. SIAM J. Numer. Anal., 47(5):3720--3743, 2009. [ bib | DOI | http | .pdf ]
[32] Sören Bartels. Semi-implicit approximation of wave maps into smooth or convex surfaces. SIAM J. Numer. Anal., 47(5):3486--3506, 2009. [ bib | DOI | http | .pdf ]
[31] Sören Bartels, Christian Lubich, and Andreas Prohl. Convergent discretization of heat and wave map flows to spheres using approximate discrete Lagrange multipliers. Math. Comp., 78(267):1269--1292, 2009. [ bib | DOI | http | .pdf ]
[30] Sören Bartels. Combination of global and local approximation schemes for harmonic maps into spheres. J. Comput. Math., 27(2-3):170--183, 2009. [ bib | www: ]
[29] Sören Bartels and Tomáš Roubíček. Thermoviscoplasticity at small strains. ZAMM Z. Angew. Math. Mech., 88(9):735--754, 2008. [ bib | DOI | http | .pdf ]
[28] Sören Bartels and Andreas Prohl. Convergence of an implicit, constraint preserving finite element discretization of p-harmonic heat flow into spheres. Numer. Math., 109(4):489--507, 2008. [ bib | DOI | http | .pdf ]
[27] L'ubomír Baňas, Sören Bartels, and Andreas Prohl. A convergent implicit finite element discretization of the Maxwell-Landau-Lifshitz-Gilbert equation. SIAM J. Numer. Anal., 46(3):1399--1422, 2008. [ bib | DOI | http | .pdf ]
[26] Sören Bartels, Joy Ko, and Andreas Prohl. Numerical analysis of an explicit approximation scheme for the Landau-Lifshitz-Gilbert equation. Math. Comp., 77(262):773--788, 2008. [ bib | DOI | http | .pdf ]
[25] Sören Bartels and Carsten Carstensen. A convergent adaptive finite element method for an optimal design problem. Numer. Math., 108(3):359--385, 2008. [ bib | DOI | http | .pdf ]
[24] Sören Bartels, Xiaobing Feng, and Andreas Prohl. Finite element approximations of wave maps into spheres. SIAM J. Numer. Anal., 46(1):61--87, 2007/08. [ bib | DOI | http | .pdf ]
[23] Sören Bartels and Andreas Prohl. Stable discretization of scalar and constrained vectorial Perona-Malik equation. Interfaces Free Bound., 9(4):431--453, 2007. [ bib | DOI | http | .pdf ]
[22] Sören Bartels and Andreas Prohl. Constraint preserving implicit finite element discretization of harmonic map flow into spheres. Math. Comp., 76(260):1847--1859, 2007. [ bib | DOI | http | .pdf ]
[21] John W. Barrett, Sören Bartels, Xiaobing Feng, and Andreas Prohl. A convergent and constraint-preserving finite element method for the p-harmonic flow into spheres. SIAM J. Numer. Anal., 45(3):905--927, 2007. [ bib | DOI | http | .pdf ]
[20] Sören Bartels, Carsten Carstensen, Sergio Conti, Klaus Hackl, Ulrich Hoppe, and Antonio Orlando. Relaxation and the computation of effective energies and microstructures in solid mechanics. In Analysis, modeling and simulation of multiscale problems, pages 197--224. Springer, Berlin, 2006. [ bib | DOI | http | .pdf ]
[19] Sören Bartels and Andreas Prohl. Convergence of an implicit finite element method for the Landau-Lifshitz-Gilbert equation. SIAM J. Numer. Anal., 44(4):1405--1419, 2006. [ bib | DOI | http | .pdf ]
[18] S. Bartels, C. Carstensen, and A. Hecht. P2Q2Iso2D=2D isoparametric FEM in Matlab. J. Comput. Appl. Math., 192(2):219--250, 2006. [ bib | DOI | http | .pdf ]
[17] Sören Bartels. Robust a priori error analysis for the approximation of degree-one Ginzburg-Landau vortices. M2AN Math. Model. Numer. Anal., 39(5):863--882, 2005. [ bib | DOI | http | .pdf ]
[16] Sören Bartels. Reliable and efficient approximation of polyconvex envelopes. SIAM J. Numer. Anal., 43(1):363--385, 2005. [ bib | DOI | http | .pdf ]
[15] Sören Bartels. Stability and convergence of finite-element approximation schemes for harmonic maps. SIAM J. Numer. Anal., 43(1):220--238, 2005. [ bib | DOI | http | .pdf ]
[14] Sören Bartels. A posteriori error analysis for time-dependent Ginzburg-Landau type equations. Numer. Math., 99(4):557--583, 2005. [ bib | DOI | http | .pdf ]
[13] Sören Bartels and Tomáš Roubíček. Linear-programming approach to nonconvex variational problems. Numer. Math., 99(2):251--287, 2004. [ bib | DOI | http | .pdf ]
[12] S. Bartels and C. Carstensen. Averaging techniques yield reliable a posteriori finite element error control for obstacle problems. Numer. Math., 99(2):225--249, 2004. [ bib | DOI | http | .pdf ]
[11] Sören Bartels. Linear convergence in the approximation of rank-one convex envelopes. M2AN Math. Model. Numer. Anal., 38(5):811--820, 2004. [ bib | DOI | http | .pdf ]
[10] S. Bartels, C. Carstensen, K. Hackl, and U. Hoppe. Effective relaxation for microstructure simulations: algorithms and applications. Comput. Methods Appl. Mech. Engrg., 193(48-51):5143--5175, 2004. [ bib | DOI | http | .pdf ]
[9] S. Bartels, C. Carstensen, and G. Dolzmann. Inhomogeneous Dirichlet conditions in a priori and a posteriori finite element error analysis. Numer. Math., 99(1):1--24, 2004. [ bib | DOI | http | .pdf ]
[8] Sören Bartels. Adaptive approximation of Young measure solutions in scalar nonconvex variational problems. SIAM J. Numer. Anal., 42(2):505--530, 2004. [ bib | DOI | http | .pdf ]
[7] S. Bartels, C. Carstensen, P. Plecháč, and A. Prohl. Convergence for stabilisation of degenerately convex minimisation problems. Interfaces Free Bound., 6(2):253--269, 2004. [ bib | DOI | http | .pdf ]
[6] Sören Bartels and Andreas Prohl. Multiscale resolution in the computation of crystalline microstructure. Numer. Math., 96(4):641--660, 2004. [ bib | DOI | http | .pdf ]
[5] Carsten Carstensen, Sören Bartels, and Stefan Jansche. A posteriori error estimates for nonconforming finite element methods. Numer. Math., 92(2):233--256, 2002. [ bib | DOI | http | .pdf ]
[4] Sören Bartels and Carsten Carstensen. Each averaging technique yields reliable a posteriori error control in FEM on unstructured grids. II. Higher order FEM. Math. Comp., 71(239):971--994, 2002. [ bib | DOI | http | .pdf ]
[3] Carsten Carstensen and Sören Bartels. Each averaging technique yields reliable a posteriori error control in FEM on unstructured grids. I. Low order conforming, nonconforming, and mixed FEM. Math. Comp., 71(239):945--969, 2002. [ bib | DOI | http | .pdf ]
[2] Carsten Carstensen, Sören Bartels, and Roland Klose. An experimental survey of a posteriori Courant finite element error control for the Poisson equation. Adv. Comput. Math., 15(1-4):79--106 (2002), 2001. A posteriori error estimation and adaptive computational methods. [ bib | DOI | http | .pdf ]
[1] Sören Bartels, Carsten Carstensen, and Petr Plecháč. Finite element computation of macroscopic quantities in nonconvex minimisation problems and applications in materials science. In Multifield problems, pages 69--79. Springer, Berlin, 2000. [ bib | .pdf ]

Bücher

[3] Sören Bartels. Numerical approximation of partial differential equations, volume 64 of Texts in Applied Mathematics. Springer, [Cham], 2016. [ bib | DOI | http ]
[2] Sören Bartels. Numerik 3x9. Springer-Lehrbuch. Springer Spektrum, 2016. [ bib | DOI | http ]
[1] Sören Bartels. Numerical methods for nonlinear partial differential equations, volume 47 of Springer Series in Computational Mathematics. Springer, Cham, 2015. [ bib | DOI | http ]

Konferenzbeiträge

[11] Sören Bartels, Stephan Hertzog, Marijo Milicevic, and Patrick Schön. Numerical methods for optimal transportation. Oberwolfach Reports, 2017. Oberwolfach Workshop on: Emerging Effects in Interfaces and Free Boundaries. [ bib | DOI ]
[10] Sören Bartels, Andrea Bonito, and Ricardo H. Nochetto. Numerical methods for bilayer bending problems. Oberwolfach Reports, 2015. Oberwolfach Workshop on: Geometric Partial Differential Equations: Surface and Bulk Processes. [ bib | DOI ]
[9] Sören Bartels, Ricardo H. Nochetto, and Abner J. Salgado. Total variation minimization with finite elements. Oberwolfach Reports, 2013. Oberwolfach Workshop on: Interfaces and Free Boundaries: Analysis, Control and Simulation. [ bib | DOI ]
[8] Sören Bartels and Martin Kružík. An efficient approach to numerical solutions of multi-well variational problems. Oberwolfach Reports, 1(7):780--783, 2010. Oberwolfach Workshop on: Microstructures in Solids: From Quantum Models to Continua. [ bib | DOI ]
[7] Sören Bartels and Rüdiger Müller. Numerical analysis for phase field simulations of moving interfaces with topological changes. Proc. Appl. Math. Mech, 10(1), 2010. [ bib | DOI | .pdf ]
[6] Sören Bartels. Approximation of harmonic maps and wave maps. Oberwolfach Reports, 5(3):2037--2038, 2008. Oberwolfach Workshop on Nonstandard Finite Element Methods. [ bib | DOI | .pdf ]
[5] Sören Bartels, Georg Dolzmann, and Ricardo H. Nochetto. Analysis and numerical simulation of the evolution of patterns in the gel phase of lipid membranes. Oberwolfach Reports, 5(3):2318--2321, 2008. Oberwolfach Mini-Workshop on: Mathematics of Biological Membranes. [ bib | DOI ]
[4] Sören Bartels and Rüdiger Müller. Robust error estimates for adaptive phase field simulations. Proc. Appl. Math. Mech, 8(1):10983 -- 10984, 2008. [ bib | DOI | .pdf ]
[3] Sören Bartels and Rüdiger Müller. Robust a-posteriori error control of Cahn-Hilliard type equations with elasticity. Proc. Appl. Math. Mech, 7(1):1023305 -- 1023306, 2007. [ bib | DOI | .pdf ]
[2] Sören Bartels. Constraint preserving, inexact solution of implicit discretizations of Landau--Lifshitz--Gilbert equations and consequences for convergence. Proc. Appl. Math. Mech, 6(1):19--22, 2006. [ bib | DOI | .pdf ]
[1] Sören Bartels. Error estimates for the adaptive computation of a scalar three well problem. Proc. Appl. Math. Mech, 1(1):502--503, 2002. [ bib | DOI | .pdf ]

Abschlussarbeiten

[4] Sören Bartels. Finite element approximation of harmonic maps betweeen surfaces. Habilitation thesis, Humboldt Universität zu Berlin, Germany, 2009. [ bib | .pdf ]
[3] Sören Bartels. Numerical analysis of some nonconvex variational problems. Ph.D. thesis, Christian--Albrechts-Universität zu Kiel, Germany, 2001. [ bib | .pdf ]
[2] Sören Bartels. Theorie und Numerik retardierter Integralgleichungen elektromagnetischer Streufelder. Diploma thesis, Christian--Albrechts-Universität zu Kiel, Germany, 1999. [ bib | .pdf ]
[1] Sören Bartels. Numerical analysis of retarded potential integral equations of electromagnetism. Master thesis, Heriot--Watt University Edinburgh, Scotland, UK, 1998. [ bib | .pdf ]