A posteriori error bounds for discontinuous Galerkin methods for quasilinear parabolic problems

Details A posteriori error bounds for discontinuous Galerkin methods for quasilinear parabolic problems A posteriori error bounds for discontinuous Galerkin methods for quasilinear parabolic problems

2010-01-17

arxiv.org/abs/1001.2935v1

Mathematics

Numerical Analysis

8 pages, conference ENUMATH 2009

Scientific paper

We derive a posteriori error bounds for a quasilinear parabolic problem, which is approximated by the $hp$-version interior penalty discontinuous Galerkin method (IPDG). The error is measured in the energy norm. The theory is developed for the semidiscrete case for simplicity, allowing to focus on the challenges of a posteriori error control of IPDG space-discretizations of strictly monotone quasilinear parabolic problems. The a posteriori bounds are derived using the elliptic reconstruction framework, utilizing available a posteriori error bounds for the corresponding steady-state elliptic problem.

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