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85 results on '"Dietmar Gallistl"'

37. Numerical stochastic homogenization by quasilocal effective diffusion tensors

Author

Daniel Peterseim and Dietmar Gallistl

Subjects
A posteriori error estimates, Model reduction, Applied Mathematics, General Mathematics, Uncertainty, 35R60, 65N12, 65N15, 65N30, 73B27, 74Q05, Numerical Analysis (math.NA), Partial differential operator, 01 natural sciences, Homogenization (chemistry), n/a OA procedure, 010101 applied mathematics, A priori error estimates, Multiscale method, Modeling error estimate, Upscaling, FOS: Mathematics, Applied mathematics, A priori and a posteriori, Mathematics - Numerical Analysis, Boundary value problem, 0101 mathematics, Numerical homogenization, Effective response, Mathematics
Abstract

This paper proposes a numerical upscaling procedure for elliptic boundary value problems with diffusion tensors that vary randomly on small scales. The method compresses the random partial differential operator to an effective quasilocal deterministic operator that represents the expected solution on a coarse scale of interest. Error estimates consisting of a priori and a posteriori terms are provided that allow one to quantify the impact of uncertainty in the diffusion coefficient on the expected effective response of the process.

Published
2022

40. Analysis of a mixed discontinuous Galerkin method for the time-harmonic Maxwell equations with minimal smoothness requirements

Author

Kaifang Liu, Dietmar Gallistl, Matthias Schlottbom, J J W van der Vegt, Mathematics of Computational Science, and MESA+ Institute

Subjects
Computational Mathematics, Applied Mathematics, General Mathematics, FOS: Mathematics, UT-Hybrid-D, Numerical Analysis (math.NA), Mathematics - Numerical Analysis, 35R05, 35Q61, 65N12, 65N15, 65N30
Abstract

An error analysis of a mixed discontinuous Galerkin (DG) method with lifting operators as numerical fluxes for the time-harmonic Maxwell equations with minimal smoothness requirements is presented. The key difficulty in the error analysis for the DG method is that due to the low regularity the tangential trace of the exact solution is not well defined on the faces of the computational mesh. This difficulty is addressed by adopting the face-to-cell lifting introduced by Ern & Guermond (2021, Quasi-optimal nonconforming approximation of elliptic PDEs with contrasted coefficients and $H^{1+r}$, $r>0$, regularity. Found. Comput. Math., 1–36). To obtain optimal local interpolation estimates, we introduce Scott–Zhang-type interpolations that are well defined for $H(\textrm {curl})$ and $H(\textrm {div})$ functions with minimal regularity requirements. As a by-product of penalizing the lifting of the tangential jumps, an explicit and easily computable stabilization parameter is given.

Published
2022

49. Taylor--Hood Discretization of the Reissner--Mindlin Plate

Author

Mira Schedensack and Dietmar Gallistl

Subjects
Numerical Analysis, Discretization, Degree (graph theory), Applied Mathematics, Mathematical analysis, 010103 numerical & computational mathematics, Superconvergence, 01 natural sciences, Finite element method, Physics::Fluid Dynamics, Condensed Matter::Soft Condensed Matter, Computational Mathematics, Piecewise, 0101 mathematics, Rotation (mathematics), Mathematics
Abstract

A shear-locking free finite element discretization of the Reissner--Mindlin plate model is introduced. The rotation is discretized with piecewise polynomials of degree $k+2$ while the degree $k\geq...

Published
2021
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