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Publications of the Resarch Group

Recent work

  1. G. Kitzler, J. Schöberl: A polynomial spectral method for the spatially homogenous Boltzmann equation in 3 dimension, ASC Report 28/2017, Institute for Analysis and Scientific Computing, Vienna University of Technology, 2017 pdf
  2. P. L. Lederer, C. Merdon, and J. Schöberl, "Refined a posteriori error estimation for classical and pressure-robust Stokes finite element methods", arXiv:1712.01625
  3. D. Braess, A.S. Pechstein and J. Schöberl, "An Equilibration Based A Posteriori Error Estimate for the Biharmonic Equation and Two Finite Element Methods", 2017,
  1. J. Schöberl: "C++11 Implementation of Finite Elements in NGSolve", ASC Report 30/2014, Institute for Analysis and Scientific Computing, Vienna University of Technology, 2014, preprint
  2. J. Gopalakrishnan, J. Schöberl: Degree and wavenumber [in]dependence of a Schwarz preconditioner for the DPG method', To appear in ICOSAHOM 2014 Proceedings. pdf
  3. G. Kitzler, J. Schöberl: Efficient Spectral Methods for the spatially homogeneous Boltzmann equation, ASC Report 13/2013", Institute for Analysis and Scientific Computing, Vienna University of Technology, 2013 pdf
  4. J. Schöberl, C. Lehrenfeld: Domain Decomposition Preconditioning for High Order Hybrid Discontinuous Galerkin Methods on Tetrahedral Meshes,preprint p 27-56 Advanced Finite Element Methods and Applications, Lecture Notes in Applied and Computational Mechanics 66, 2012
  5. M. Huber, A. Pechstein, J. Schöberl: Hybrid Domain Decomposition Solvers for Scalar and Vectorial Wave Equation,ASC Report 15/2011
  6. L. Beirão da Veiga, C. Chinosi, C. Lovadina, L.F. Pavarino, J. Schöberl: Quasi-uniformity of BDDC preconditioners for the MITC Reissner-Mindlin problem, I.M.A.T.I.-C.N.R. (2011), 1-14, preprint
  7. G. May, J. Schöberl: Analysis of a Spectral Difference Scheme with Flux Interpolation on Raviart-Thomas Elements, AICES report 2010/04-8 preprint

Journal publications

  1. P. L. Lederer, C. Lehrenfeld, and J. Schöberl, "Hybrid Discontinuous Galerkin methods with relaxed H(div)-conformity for incompressible flows. Part I", SIAM Journal on Numerical Analysis (to appear) arXiv:1707.02782
  2. P. L. Lederer and J. Schöberl, "Polynomial robust stability analysis for H(div)-conforming finite elements for the Stokes equations", IMA Journal of Numerical Analysis, drx051, (2017),
  3. A.S. Pechstein and J. Schöberl, "An analysis of the TDNNS method using natural norms", J. Numer. Math. 139(1), 93-120 (2018).,
  4. P. L. Lederer, A. Linke, C. Merdon, and J. Schöberl, "Divergence-free Reconstruction Operators for Pressure-Robust Stokes Discretizations With Continuous Pressure Finite Elements", SIAM Journal on Numerical Analysis, Vol. 55(3), pp. 1291-1314(2017) arXiv:1609.03701
  5. A.S. Pechstein and J. Schöberl, "The TDNNS method for Reissner-Mindlin plates", J. Numer. Math. (2017) 137, pp 713-740,
  6. J. Gopalakrishnan and J. Schöberl and C. Wintersteiger, "Mapped tent pitching schemes for hyperbolic systems", SIAM J. Sci. Comput. 39-6 (2017), pp. B1043-B1063 arXiv:1604.01081
  7. C. Lehrenfeld, J. Schöberl, "High order exactly divergence-free Hybrid Discontinuous Galerkin Methods for unsteady incompressible flows", Comp Meth in Applied Mechanics and Engineering (CMAME),, 307:339 -- 361, 2016, ASC Report No. 27/2015, ASC, TU Wien, 2015, pdf
  8. G. Kitzler, J. Schöberl: A high order space momentum discontinuous Galerkin method for the Boltzmann equation, Computers & Mathematics with Applications, Volume 70, Issue 7, October 2015, Pages 1539-1554 ASC-preprint
  9. CH. Brennecke, A. Linke, Ch. Merdon, J. Schöberl, Optimal and pressure-independent L2 velocity error estimates for a modified Crouzeix--Raviart Stokes element with BDM reconstructions, J. Comput. Math., 33 (2015) pp. 191--208.
  10. Halla, M., Hohage, T., Nannen, L., Schöberl, J. (2015) Hardy Space Infinite Elements for Time Harmonic Wave Equations with Phase and Group Velocities of Different Signs. Numerische Mathematik, 2015 online.
  11. M. Brandstetter, M. Liertzer, C. Deutsch, P. Klang, J. Schöberl, H.E. Tureci, G. Strasse, K. Unterrainer, S. Rotter (2014) Reversing the pump dependence of a laser at an exceptional point, Nature Communications, Vol 5, article nr 4034, Jun 2014 link
  12. I. Sakalli, J. Schöberl, and E.W. Knapp: mFES: A Robust Molecular Finite Element Solver for Electrostatic Energy Computations, Journal of Chemical Theory and Computation JCTC, Vol 10, pp 5095-5112, 2014, link
  13. K.-A. Mardal, J. Schöberl and R. Winther: A uniformly stable Fortin operator for the Taylor–Hood element, Numerische Mathematik, Vol 123(3), pp 537-551 preprint
  14. Nannen, L. , Hohage, T. , Schädle, A., Schöberl. J. Exact Sequences of High Order Hardy Space Infinite Elements for Exterior Maxwell Problems, SIAM J. Scientific Computing, 35(2): A1024-A1048, 2013, online, arxiv, extended abstract.
  15. A. Pechstein, J. Schöberl: Anisotropic mixed finite elements for elasticity, International Journal for Numerical Methods in Engineering, Vol 90(2), pp 196-217 (2012) [http:DOI:10.1002/nme.3319 doi], preprint
  16. A. Balan, G. May and J. Schöberl: A Stable High-Order Spectral Difference Method for Hyperbolic Conservation Laws in Triangular Elements., Journal of Computational Physics, Vol 231(5), 2359-2375 (2012) DOI: 10.1016/
  17. L. Demkowicz, J. Gopalakrishnan, J. Schöberl: Polynomial Extension Operators. Part III. Mathematics of Computation, Vol. 81 (2012), 1289-1326, DOI: 10.1090/S0025-5718-2011-02536-6,preprint
  18. A. Pechstein, J. Schöberl: Tangential-Displacement and Normal-Normal-Stress Continuous Mixed Finite Elements for Elasticity. Mathematical Models and Methods in Applied Sciences (M3AS) Vol 21(8), pp 1761-1782 (2011) DOI: 10.1142/S0218202511005568 extended preprint
  19. J. Schöberl, R. Simon, W. Zulehner: A Robust Multigrid Method for Elliptic Optimal Control Problems. SIAM J Numerical Analysis Vol 49(4), pp 1482-1503 (2011) DOI: 10.1137/100783285 preprint]
  20. A Hannukainen, M. Huber and J. Schöberl: A Mixed Hybrid Finite Element Method for the Helmholtz Equation. Journal of Modern Optics Vol. 58, Nos. 5-6, 424-437 (2011) DOI: 10.1080/09500340.2010.527067 preprint
  21. H. Egger, M. Hanke, C. Schneider, J. Schöberl, S. Zaglmlayr: Adjoint based sampling methods for electromagnetic scattering. Inverse Problems 26 (2010) 074006 preprint
  22. P. Monk, J. Schöberl, A. Sinwel: Hybridizing Raviart-Thomas elements for the Helmholtz equation. Electromagnetics, Vol 30(1), pages 149-176 (2010) preprint
  23. H. Egger, J. Schöberl: A Mixed-Hybrid-Discontinuous Galerkin Finite Element Method for Convection-Diffusion Problems. IMA Journal of Numerical Analysis, Vol 30(4), 1206-1234 (2010) preprint
  24. L. Demkowicz, J. Gopalakrishnan, J. Schöberl: Polynomial Extension Operators. Part II. SIAM J Numerical Analysis, Vol 47(5), pages 3293-3324 (2009) preprint
  25. R.H.W. Hoppe, J. Schöberl: Convergence of Adaptive Edge Element Methods for the 3D Eddy Current Equations. Journal of Computational Mathematics, Vol 27, pages 657-676 (2009) preprint
  26. J. Schöberl, R. Stenberg: Multigrid Methods for Stabilized Reissner Mindlin Plate Formulations. SIAM J Numerical Analysis, Vol 47(4), pages 2735-2751 (2009) preprint
  27. D. Braess, J. Schöberl, V. Pillwein: Equilibrated Residual Error Estimates are p-Robust. Computer Methods in Applied Mechanics and Engineering, Vol 198, pages 1189-1197 (2009) preprint
  28. M. Huber, J. Schöberl, A. Sinwel, S. Zaglmayr: Simulation of Diffraction in periodic Media with a coupled Finite Element and Plane Wave Approach SIAM J Scientific Computing, 31(2), pages 1500-1517, 2009, preprint
  29. L. Demkowicz, J. Gopalakrishnan, J. Schöberl: Polynomial Extension Operators. Part I. SIAM J Numerical Analysis, Vol 46(6), 3006-3031, 2008 preprint
  30. D. Braess, R.H.W. Hoppe, J. Schöberl: A posteriori estimators for obstacle problems by the hypercircle method Computing and Visualization in Science , 11(4-6), pages 351-362, 2008. preprint
  31. D. Braess and J. Schöberl: Equilibrated Residual Error Estimator for Maxwell's Equations. Mathematics of Computation, Vol 77(262), 651-672, 2008 preprint
  32. J. Schöberl: A posteriori error estimates for Maxwell Equations. Mathematics of Computation, Vol 77(262), 633-649, 2008 preprint
  33. J. Schöberl, J. Melenk, C. Pechstein, and S. Zaglmayr: Additive Schwarz Preconditioning for p-Version Triangular and Tetrahedral Finite Elements IMA Journal of Numerical Analysis, Vol 28, pages 1-24,2008 preprint
  34. M. Schinnerl, M. Kaltenbacher, U. Langer, R. Lerch, and J. Schöberl. Numerical Simulation of Magneto-Mechanical Sensors and Actuators. Surveys on Mathematics for Industry, 18(2), 223-271, 2007} preprint
  35. J. Schöberl and W. Zulehner: Symmetric Indefinite Preconditioners for saddle Point Problems with Applications to PDE-Constrained Optimization Problems. SIAM Journal on Matrix Analysis and Applications, Vol 29(3), pages 752-773, 2007 preprint
  36. S. Hein, T. Hohage, W. Koch, and J. Schöberl: Acoustic Resonacnes in a High Lift Configuration. Journal of Fluid Mechanics 582, pages 179-202, 2007 preprint
  37. A. Becirovic, P. Paule, V. Pillwein, A. Riese, C. Schneider, and J.Schöberl: Hypergeometric Summation Algorithms for High-order Finite Elements. Computing, 78(3), pages 235-249, 2006 preprint
  38. S. Beuchler and J. Schöberl: New shape functions for triangular p-FEM using integrated Jacobi polynomials Numerische Mathematik 103(3), pages 339-366, 2006 preprint
  39. D. Boffi, F. Kikuchi, and J. Schöberl: Edge element computation of Maxwell's eigenvalues on general quadrilateral meshes. Mathematical Models and Methods in Applied Sciences 16:265-273, 2006 preprint
  40. C. Carstensen and J. Schöberl: Residual-based a posteriori error estimate for a mixed Reissner-Mindlin plate finite element method. Numerische Mathematik 103(2), pages 225-250, 2006 preprint
  41. J. Gerstmayr and J. Schöberl: A 3D finite element method for flexible multibody systems. Multibody System Dynamics, 15, pages 309-324, 2006 preprint
  42. M. Hofer, N. Finger, G. Kovacs, J. Schöberl, S. Zaglmayr, U. Langer, and R. Lerch: Finite Element Simulation of Wave Propagation in Periodic Piezoelectric SAW Structures. IEEE Transactions on UFFC, 53(6), pages 1192-1201, 2006 preprint
  43. F. Bachinger, U. Langer, and J. Schöberl: Efficient Solvers for Nonlinear Time-Periodic Eddy Current Problems. Computing and Visualization in Science, 9(4), pages 197-207, 2006 preprint
  44. J. Schöberl and S. Zaglmayr: High order Nedelec elements with local complete sequence properties. International Journal for Computation and Mathematics in Electrical and Electronic Engineering (COMPEL), 24(2), pages 374-384, 2005 preprint
  45. F. Bachinger, U. Langer, and J. Schöberl: Numerical Analysis of Nonlinear Multiharmonic Eddy Current Problems. Numerische Mathematik. 100(4), pages 594-616, 2005 preprint
  46. S. Beuchler and J. Schöberl: Optimal extensions on tensor-product meshes. Applied Numerical Mathematics 54(3-4), pages 391-405, 2005 preprint
  47. Z. Dostal and J. Schöberl: Minimizing quadratic functions over non-negative cone with the rate of convergence and finite termination. Computational Optimization and Applications 30(1), pages 23-44, 2005 preprint
  48. R.D. Lazarov, J.E. Pasciak, J. Schöberl, and P.S. Vassilevski: Almost optimal interior penalty discontinuous approximations of symmetric elliptic problems on non-matching grids. Numerische Mathematik 96, pages 295-315, 2003 preprint
  49. J. Schöberl and W. Zulehner: On Schwarz-type Smoothers for Saddle Point Problems. Numerische Mathematik 95(2), pages 377-399, 2003 preprint
  50. S. Reitzinger and J. Schöberl: Algebraic Multigrid for Edge Elements. Numerical Linear Algebra with Applications 9(3), pages 223-238, 2002 preprint
  51. M. Schinnerl, J. Schöberl, M. Kaltenbacher, and R. Lerch: Multigrid Methods for the 3D Simulation of Nonlinear Magneto-Mechanical Systems. IEEE Transactions Magnetics 38(3), pages 1497-1511, 2002 preprint
  52. T. Apel and J. Schöberl: Multigrid Methods for Anisotropic Edge Refinement SIAM Journal on Numerical Analyis 40(5), pages 1993-2006, 2002 preprint
  53. B. Kaltenbacher and J. Schöberl: A Saddle Point Variational Formulation for Projection-Regularized Parameter Identification. Numerische Mathematik 91(4), pages 675-697, 2002 preprint
  54. T. Apel, S. Nicaise, and J. Schöberl: A non-conforming finite element method with anisotropic mesh grading for the Stokes problem in domains with edges. IMA Journal of Numerical Analysis 21, pages 843-856, 2001 preprint
  55. T. Apel, S. Nicaise, and J. Schöberl: Crouzeix-Raviart type finite elements on anisotropic meshes. Numerische Mathematik 89(2), pages 193-223, 2001 preprint
  56. J. Schöberl: Efficient Contact Solvers Based on Domain Decomposition Techniques. Computers & Mathematics with Applications 42, pages 1217-1228, 2001 preprint
  57. G. Haase, U. Langer, S. Reitzinger, and J. Schöberl: Algebraic Multigrid Methods based on Element Preconditioning. International Journal of Computer Mathematics 78(4): pages 676-598, 2001 preprint
  58. J. Schöberl: Multigrid Methods for a Parameter Dependent Problem in Primal Variables. Numerische Mathematik , 84(1), pages 97-119 (1999) preprint
  59. J. Schöberl: Solving the Signorini Problem on the Basis of Domain Decomposition Techniques. Computing, 60(4), pages 323-344, 1998. preprint
  60. J. Schöberl: NETGEN - An advancing front 2D/3D-mesh generator based on abstract rules. Computing and Visualization in Science, 1(1), pages 41-52, 1997. preprint

Proceedings and Book Chapters

  1. K. Hollaus, J. Schöberl, "Homogenization of the Eddy Current Problem in 2D," Proceedings of the 14th International IGTE Symposium on Numerical Field Calculation in Electrical Engineering, pp. 154-159, Graz, Austria, September 19-22, 2010. preprint
  2. P.G. Gruber, J. Kienesberger, U. Langer, J. Schöberl, J. Valdman: Fast Solvers and A Posteriori Error Estimates in Elastoplasticity. in: Numerical and Symbolic Scientific Computing: Progress and Prospects, Ulrich Langer and Peter Paule (ed.), pp. 45-64. 2011. Springer, Wien, ISBN-13: 978-3709107935 preprint
  3. S. Beuchler, V. Pillwein, J. Schöberl and S. Zaglmayr: Sparsity optimized high order finite element functions on simplices in: Numerical and Symbolic Scientific Computing: Progress and Prospects, Ulrich Langer and Peter Paule (ed.), pp. 21-44. 2011. Springer, Wien, ISBN-13: 978-3709107935 preprint
  4. C Koutschan, C Lehrenfeld, J. Schöberl: Computer Algebra meets Finite Elements: an Efficient Implementation for Maxwell's Equations in: Numerical and Symbolic Scientific Computing: Progress and Prospects, Ulrich Langer and Peter Paule (ed.), pp. 105-122. 2011. Springer, Wien, ISBN-13: 978-3709107935 arxiv:1104.4208
  5. A. Balan, G. May and J. Schöberl: A Stable Spectral Difference Method for Triangles, AIAA paper number 2011-47, 49th American Institute of Aeronautics and Astronautics Aerospace Sciences Meeting, Orlando, Florida, January 2011 preprint
  6. K. Hollaus, D. Feldengut, J. Schöberl, M. Wabro, D. Omeragic: Nitsche-type Mortaring for Maxwell's Equations PIERS Proceedings, 397 - 402, July 5-8, Cambridge, USA 2010 preprint
  7. J. Schöberl: A multilevel decomposition result in H(curl). in Multigrid, Multilevel and Multiscale Methods, EMG 2005 CD, Eds: P. Wesseling, C.W. Oosterlee, P. Hemker, ISBN 90-9020969-7, preprint
  8. S. Zaglmayr, J. Schöberl, and U. Langer: Eigenvalue Problems in Surface Acoustic Wave Filter Simulation. Progress in Industrial Mathematics at ECMI 2004, pp. 75-99, Springer Verlag, Nov. 2005, preprint
  9. ...

Technical Reports

  1. J. Schöberl: Commuting quasi-interpolation operators for mixed finite elements. Preprint ISC-01-10-MATH, Institute for Scientific Computing, Texas A&M University, 2001, pdf
  2. ...


  • J. Schöberl: Robust Multigrid Methods for Parameter Dependent Problems, Dissertation, Johannes Kepler Universität Linz, 1999 pdf

the linked pdf-files are preprint versions and may differ from the original journal publications