Author:
Georgoulis Emmanuil H.,Lakkis Omar,Wihler Thomas P.
Abstract
AbstractWe 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.
Publisher
Springer Science and Business Media LLC
Subject
Applied Mathematics,Computational Mathematics
Cited by
3 articles.
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