Numerik-Praktikum

Lecture "Numerical Methods for Singularly Perturbed Differential Equations

SS 2024

WS 2023/2024

SS 2023

WS 2022/2023

SS 2022

WS 2021/2022

SS 2020

Publikationen

• D. Gallistl and M. Schedensack:
  Residual-based a posteriori error analysis of a Taylor–Hood discretization of the Reissner–Mindlin plate,
  ESAIM, Math. Model. Numer. Anal., volume 59, pp.2005–2019, 2025. [bibtex] [doi]
• P. Bringmann, Jonas W. Ketteler and M. Schedensack:
  Discrete Helmholtz decompositions of piecewise constant and piecewise affine vector and tensor fields,
  Found. Comput. Math., volume 25, pp.417–461, 2025. [bibtex] [doi]
• C. Carstensen and M. Schedensack:
  Two Discretisations of the Time-Dependent Bingham Problem,
  Numer. Math., volume 153, no.2–3, pp.411–450, 2023. [bibtex] [doi]
• J. Riesselmann, J. Ketteler, M. Schedensack and D. Balzani:
  Rot-free mixed finite elements for gradient elasticity at finite strains,
  Internat. J. Numer. Methods Engrg., volume 122, no.6, pp.1602–1628, 2021. [bibtex] [doi]
• D. Gallistl and M. Schedensack:
  Taylor–Hood discretization of the Reissner–Mindlin plate,
  SIAM J.\ Numer.\ Anal., volume 59, no.3, pp.1195–1217, 2021. [bibtex] [doi]
• D. Gallistl and M. Schedensack:
  A robust discretization of the Reissner–Mindlin plate with arbitrary polynomial degree,
  J. Comput. Math., volume 38, pp.1–13, 2020. [bibtex] [doi]
• J. Riesselmann, J. Ketteler, M. Schedensack and D. Balzani:
  Three-field mixed finite element formulations for gradient elasticity at finite strains,
  GAMM-Mitteilungen, 2019. (Published online.) [bibtex] [doi]
• J. Hu and M. Schedensack:
  Two low-order nonconforming finite element methods for the Stokes flow in 3D,
  IMA J. Numer. Anal., volume 39, no.3, pp.1447–1470, 2019. [bibtex] [doi]
• Li, G., Peterseim, D. and Schedensack, M.:
  Error analysis of a variational multiscale stabilization for convection-dominated diffusion equations in two dimensions,
  IMA J. Numer. Anal., volume 38, no.3, pp.1229–1253, 2018. [bibtex] [doi]
• Alaeian, H., Schedensack, M., Bartels, C., Peterseim, D. and Weitz, M.:
  Thermo-optical interactions in a dye-microcavity photon Bose-Einstein condensate,
  New Journal of Physics, volume 19, 2017. [bibtex] [doi]
• D. Peterseim and M. Schedensack:
  Relaxing the CFL condition for the wave equation on adaptive meshes,
  J. Sci. Comput., volume 72, no.3, pp.1196–1213, 2017. [bibtex] [doi]
• M. Schedensack:
  Mixed finite element methods for linear elasticity and the Stokes equations based on the Helmholtz decomposition,
  ESAIM Math. Model. Numer. Anal., volume 51, no.2, pp.399–425, 2017. [bibtex] [doi]
• M. Schedensack:
  A new generalization of the ${P}_1$ non-conforming FEM to higher polynomial degrees,
  Comput. Methods Appl. Math., volume 17, no.1, pp.161–185, 2017. [bibtex] [doi]
• M. Schedensack:
  A new discretization for $m$th-Laplace equations with arbitrary polynomial degrees,
  SIAM J.\ Numer.\ Anal., volume 54, no.4, pp.2138–2162, 2016. [bibtex] [doi]
• C. Kreuzer and M. Schedensack:
  Instance optimal Crouzeix-Raviart adaptive finite element methods for the Poisson and Stokes Problems,
  IMA J. Numer. Anal., volume 36, no.2, pp.593–617, 2016. [bibtex] [doi]
• C. Carstensen, B.D. Reddy and M. Schedensack:
  A natural nonconforming method for the Bingham flow is quasi-optimal,
  Numer. Math., volume 133, no.1, pp.37–66, 2016. [bibtex] [doi]
• Carstensen, C., Gallistl, D. and Schedensack, M.:
  $L^2$ best-approximation of the elastic stress in the Arnold-Winther FEM,
  IMA J. Numer. Anal., volume 36, no.3, pp.1096–1119, 2016. [bibtex] [url] [doi]
• C. Carstensen, K. Köhler, D. Peterseim and M. Schedensack:
  Comparison results for the Stokes equations,
  Appl.\ Numer.\ Math., volume 95, pp.118–129, 2015. [bibtex] [doi]
• C. Carstensen and M. Schedensack:
  Medius Analysis and Comparison results for first-order finite element methods in linear elasticity,
  IMA J. Numer. Anal., volume 35, no.4, pp.1591–1621, 2015. [bibtex] [doi]
• Carstensen, C., Gallistl, D. and Schedensack, M.:
  Adaptive nonconforming Crouzeix-Raviart FEM for eigenvalue problems,
  Math. Comp., volume 84, no.293, pp.1061–1087, 2015. [bibtex] [doi]
• Gallistl, D., Schedensack, M. and Stevenson, R. P.:
  A remark on newest vertex bisection in any space dimension,
  Comput. Methods Appl. Math., volume 14, no.3, pp.317–320, 2014. [bibtex] [doi]
• Carstensen, C., Gallistl, D. and Schedensack, M.:
  Quasi-optimal adaptive pseudostress approximation of the Stokes equations,
  SIAM J. Numer. Anal., volume 51, no.3, pp.1715–1734, 2013. [bibtex] [doi]
• Carstensen, C., Gallistl, D. and Schedensack, M.:
  Discrete reliability for Crouzeix–Raviart FEMs,
  SIAM J. Numer. Anal., volume 51, no.5, pp.2935–2955, 2013. [bibtex] [doi]
• C. Carstensen, D. Peterseim and M. Schedensack:
  Comparison results of finite element methods for the Poisson model problem,
  SIAM J.\ Numer.\ Anal., volume 50, no.6, pp.2803–2823, 2012. [bibtex] [doi]

• J. Riesselmann, J. Ketteler, M. Schedensack and D. Balzani:
  Robust and Efficient Finite Element Discretizations for Higher-Order Gradient Formulations,
  In Non-standard Discretisation Methods in Solid Mechanics, Springer, New York, volume 98, pp.69–90, 2022. [bibtex] [doi]
• J. Riesselmann, J. Ketteler, M. Schedensack and D. Balzani:
  Rot-free finite elements for gradient-enhanced formulations at finite strains,
  In PAMM Proc. Appl. Math. Mech., volume 20, 2021. [bibtex] [doi]
• J. Riesselmann, J. Ketteler, M. Schedensack and D. Balzani:
  A New C0-Continuous FE-Formulation for Finite Gradient Elasticity,
  In PAMM Proc. Appl. Math. Mech., volume 19, 2019. [bibtex] [doi]
• J. Riesselmann, J. Ketteler, M. Schedensack and D. Balzani:
  C0 continuous finite elements for gradient elasticity at finite strains,
  In Proceedings of the 8th GACM Colloquium on Computational Mechanics for Young Scientists from Academia and Industry, pp.27–30, 2019. [bibtex] [doi]
• M. Schedensack:
  Robust discretization of the Reissner–Mindlin plate with Taylor–Hood FEM,
  In Oberwolfach Reports, volume 15, no.4, pp.2871–2872, 2018. [bibtex] [doi]
• M. Schedensack:
  Instance optimal Crouzeix-Raviart adaptive FEM for the Poisson and Stokes problems,
  In Oberwolfach Reports, volume 13, no.3, pp.2552–2554, 2016. [bibtex] [doi]
• M. Schedensack:
  An optimal AFEM for higher-order problems,
  In Oberwolfach Reports, volume 13, no.3, pp.2450–2451, 2016. [bibtex] [doi]
• S.C. Brenner, M. Oh, S. Pollock, K. Porwal, M. Schedensack and N.S. Sharma:
  A ${C}^0$ Interior Penalty Method for Elliptic Optimal Control Problems with Pointwise State Constraints in Three Dimensions,
  In Topics in Numerical Partial Differential Equations and Scientific Computing, Springer, New York, volume 160, pp.1–22, 2016. [bibtex] [doi]
• D. Peterseim and M. Schedensack:
  Relaxing the CFL condition for the wave equation on adaptive meshes,
  In PAMM Proc. Appl. Math. Mech., volume 16, pp.765–766, 2016. [bibtex] [doi]
• M. Schedensack:
  A class of mixed finite element methods based on the Helmholtz decomposition,
  In Oberwolfach Reports, volume 12, no.3, pp.2555–2556, 2015. [bibtex] [doi]
• M. Schedensack:
  Adaptive nonconforming Crou\-zeix-Raviart FEM for eigenvalue problems,
  In Oberwolfach Reports, volume 10, no.4, pp.3270–3272, 2013. [bibtex] [doi]
• M. Schedensack:
  Comparison results for first-order FEMs,
  In Oberwolfach Reports, volume 9, no.1, pp.495–497, 2012. [bibtex] [doi]

• Mira Schedensack:
  A class of mixed finite element methods based on the Helm\-holtz decomposition in computational mechanics, PhD thesis, Humboldt-Universität zu Berlin, Mathematisch-Naturwissenschaftliche Fakultät, 2015. [bibtex] [doi]
• Mira Schedensack:
  Vergleichbarkeitssätze verschiedener Finite-Elemente-Me\-tho\-den erster Ordnung (Comparison results of first-order finite element methods), PhD thesis, Humboldt-Universität zu Berlin, 2012. [bibtex]