NAApr 1, 2019
Space-time approximation of parabolic systems with variable growthDominic Breit, Prince Romeo Mensah
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 $(α_t, α_x)$-Hölder continuous.
NAApr 15, 2015
Convergence Analysis for a Finite Element Approximation of a Steady Model for Electrorheological FluidsLuigi C. Berselli, Dominic Breit, Lars Diening
In this paper we study the finite element approximation of systems of $p(\cdot)$-Stokes type, where $p(\cdot)$ is a (non constant) given function of the space variables. We derive --in some cases optimal-- error estimates for finite element approximation of the velocity and of the pressure, in a suitable functional setting.