Space-time approximation of parabolic systems with variable growth
Dominic Breit, Prince Romeo Mensah · IMA Journal of Numerical Analysis · 2019
Abstract We study a parabolic system with $p(t,x)$-structure under Dirichlet boundary conditions. In particular, we deduce the optimal convergence rate for the error of the gradient of a finite element-based space-time approximation. The error is measured in the quasi norm and the result holds if the exponent $p(t,x)$ is $(\alpha _t,\alpha _x)$-Hölder continuous.