A posteriori error analysis for time-dependent Ginzburg-Landau type equations
Ginzburg-Landau type equations are considered in a bounded Lipschitz domain in two and three space dimensions. In is shown that an adaptive finite element method based on a posteriori error estimates allows automatic mesh and time step size refinement. An upper bound for the error is computed in each time step using a post processing procedure which consits in solving a self-adjoint eigenvalue problem. The dependance of the error estimate on the parameter epsilon is explicitely determined and can be used in to define local mesh refinement indicators. Three numerical examples for Allen-Cahn and Ginzburg-Landau equations in two spatial dimensions illustrate typical properties of the approach.
scientific article; zbMATH DE number 2155987