A posteriori error bounds for fully-discrete hp-discontinuous Galerkin timestepping methods for parabolic problems

Emmanuil H. Georgoulis, Omar Lakkis, Thomas P. Wihler

Type: Article

Publication Date: 2021-04-13

Citations: 5

DOI: https://doi.org/10.1007/s00211-021-01187-7

Abstract

Abstract We 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 "Equation missing"- and "Equation missing"-type norms when I is the temporal and "Equation missing" 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 "Equation missing" norm.

Locations

Numerische Mathematik - View - PDF
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