Space-time approximation of parabolic systems with variable growth
arXiv:1804.0609714 citations
Originality Synthesis-oriented
AI Analysis
Provides theoretical error bounds for numerical solutions of parabolic PDEs with non-standard growth, relevant to applied mathematicians and engineers.
The paper derives optimal convergence rates for the gradient error of a finite element space-time approximation of parabolic systems with variable p(t,x)-growth, under Hölder continuity of the exponent.
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.