research areas

• numerical analysis
• computational partial differential equations
• a posteriori analysis and adaptive finite element methods
• nonconforming finite element methods
• higher-order problems
• computational mechanics

Publications

Articles

Research Articles (Journals)

• Riesselmann, Johannes, Ketteler, Jonas Wilhelm, Schedensack, Mira, and Balzani, Daniel. 2019. “Three‐field mixed finite element formulations for gradient elasticity at finite strains.” GAMM-Mitteilungen, № xxx doi: 10.1002/gamm.202000002.
• Li, G., Peterseim, D., and Schedensack, M. 2018. “Error analysis of a variational multiscale stabilization for convection-dominated diffusion equations in two dimensions.” IMA Journal of Numerical Analysis, № 38 (3): 1229–1253. doi: 10.1093/imanum/drx027.
• Hu, Jun, and Schedensack, Mira. 2018. “Two low-order nonconforming finite element methods for the Stokes flow in 3D.” IMA Journal of Numerical Analysis, № xxx doi: 10.1093/imanum/dry021.
• Schedensack, M. 2017. “Mixed finite element methods for linear elasticity and the Stokes equations based on the Helmholtz decomposition.” ESAIM: Mathematical Modelling and Numerical Analysis, № 51 (2): 399–425. doi: 10.1051/m2an/2016024.
• Peterseim, D., and Schedensack, M. 2017. “Relaxing the CFL Condition for the Wave Equation on Adaptive Meshes.” Journal of Scientific Computing, № 72 (3): 1196–1213. doi: 10.1007/s10915-017-0394-y.
• Schedensack, M. 2017. “A New Generalization of the P1 Non-Conforming FEM to Higher Polynomial Degrees.” Computational Methods in Applied Mathematics, № 17 (1): 161–185. doi: 10.1515/cmam-2016-0031.
• Alaeian, Hadiseh, Schedensack, Mira, Bartels, Clara, Peterseim, Daniel, and Weitz, Martin. 2017. “Thermo-optical interactions in a dye-microcavity photon Bose-Einstein condensate.” New Journal of Physics, № 19 doi: 10.1088/1367-2630/aa964c.
• Carstensen, C., Reddy, B., and Schedensack, M. 2016. “A natural nonconforming FEM for the Bingham flow problem is quasi-optimal.” Numerische Mathematik, № 133 (1): 37–66. doi: 10.1007/s00211-015-0738-1.
• Schedensack, M. 2016. “A new discretization for mth-Laplace equations with arbitrary polynomial degrees.” SIAM Journal on Numerical Analysis, № 54 (4): 2138–2162. doi: 10.1137/15M1013651.
• Kreuzer, C., and Schedensack, M. 2016. “Instance optimal Crouzeix-Raviart adaptive finite element methods for the Poisson and Stokes problems.” IMA Journal of Numerical Analysis, № 36 (2): 593–617. doi: 10.1093/imanum/drv019.
• Carstensen, C., Gallistl, D., and Schedensack, M. 2016. “L2 best approximation of the elastic stress in the Arnold-Winther FEM.” IMA Journal of Numerical Analysis, № 36 (3): 1096–1119. doi: 10.1093/imanum/drv051.
• Carstensen, C., Köhler, K., Peterseim, D., and Schedensack, M. 2015. “Comparison results for the Stokes equations.” Applied Numerical Mathematics, № 95: 118–129. doi: 10.1016/j.apnum.2013.12.005.
• Carstensen, C., Gallistl, D., and Schedensack, M. 2015. “Adaptive nonconforming Crouzeix-Raviart FEM for eigenvalue problems.” Mathematics of Computation, № 84 (293): 1061–1087. doi: 10.1090/S0025-5718-2014-02894-9.
• Carstensen, C., and Schedensack, M. 2015. “Medius analysis and comparison results for first-order finite element methods in linear elasticity.” IMA Journal of Numerical Analysis, № 35 (4): 1591–1621. doi: 10.1093/imanum/dru048.
• Gallistl, D., Schedensack, M., and Stevenson, R. 2014. “A remark on newest vertex bisection in any space dimension.” Computational Methods in Applied Mathematics, № 14 (3): 317–320. doi: 10.1515/cmam-2014-0013.
• Carstensen, C., Gallistl, D., and Schedensack, M. 2013. “Discrete reliability for Crouzeix-Raviart FEMs.” SIAM Journal on Numerical Analysis, № 51 (5): 2935–2955. doi: 10.1137/130915856.
• Carstensen, C., Gallistl, D., and Schedensack, M. 2013. “Quasi-optimal adaptive pseudostress approximation of the Stokes equations.” SIAM Journal on Numerical Analysis, № 51 (3): 1715–1734. doi: 10.1137/110852346.
• Carstensen, C, Peterseim, D, and Schedensack, M. 2012. “Comparison results of finite element methods for the Poisson model problem.” SIAM J. Numer. Anal., № 50 (6): 2803–2823. doi: 10.1137/110845707.

Research Article (Book Contributions)

• Brenner, S., Oh, M., Pollock, S., Porwal, K., Schedensack, M., and Sharma, N. 2016. “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, Vol. 160 of The IMA Volumes in Mathematics and its Applications, edited by Brenner Susanne C.. doi: 10.1007/978-1-4939-6399-7.

Theses (Doctoral or Postdoctoral)

• Schedensack, M. 2015. “A class of mixed finite element methods based on the Helmholtz decomposition in computational mechanics.” Dissertation thesis, Humboldt-Universität zu Berlin.