Numerical solution for a parabolic obstacle problem with nonsmooth initial data

Abstract

This article discusses the finite element approximation of solutions to a variational inequality of a parabolic obstacle problem with a nonsmooth initial data by a piecewise linear finite element discretization in space and an implicit time‐stepping scheme. We show that the error of the approximation in a certain norm is of order by regularization method under some realistic regularity assumptions on the exact solution, where is the time step and h is the mesh parameter of the spatial partition. Numerical examples are presented to confirm our theoretical results. © 2014 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 30: 1740–1754, 2014