Georgoulis2021_Article_APosterioriErrorBoundsForFully.pdf (429.2 kB)
A posteriori error bounds for fully-discrete hp-discontinuous Galerkin timestepping methods for parabolic problems
Version 2 2023-06-12, 09:43
Version 1 2023-06-09, 23:01
journal contribution
posted on 2023-06-12, 09:43 authored by Emmanuil H Georgoulis, Omar LakkisOmar Lakkis, Thomas P WihlerWe consider fully discrete time-space approximations of abstract linear parabolic partial differential equations (PDEs) consisting of an $hp$-version discontinuous Galerkin (DG) time-stepping scheme in conjunction with standard (conforming) Galerkin discretizations in space. We derive abstract computable a posteriori error bounds resulting, for instance, in concrete bounds in $\operatorname L_{\infty}(I;\operatorname L2(\Omega))$- and $\operatorname L_{2}(I;\operatorname H^{1}(\Omega))$-type norms when $I$ is the temporal and $\Omega$ the spatial domain for the PDE. We base our methodology for the analysis on a novel space-time reconstruction approach. Our approach is flexible as it works for any type of elliptic error estimator and leaves their choice to the user. It also exhibits mesh-change estimators in a clear and concise way. We also show how our approach allows the derivation of such bounds in the $\operatorname{H}^1(I;\opeartorname{H}^{-1}(\Omega))$ norm.
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- Published
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Numerische MathematikISSN
0029-599XPublisher
SpringerExternal DOI
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- Mathematics Publications
Full text available
- Yes
Peer reviewed?
- Yes
Legacy Posted Date
2021-02-09First Open Access (FOA) Date
2021-05-14First Compliant Deposit (FCD) Date
2021-02-09Usage metrics
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