Parabolic Finite Volume Element Equations in Nonconvex Polygonal Domains

We study spatially semidiscrete and fully discrete finite volume element approximations of the heat equation with homogeneous Dirichlet boundary conditions in a plane polygonal domain with one reentrant corner. We show that, as a result of the singularity in the solution near the reentrant corner, the convergence rate is reduced from optimal second order, similarly to what was shown for the finite element method in the earlier work [5]. Optimal order convergence may be restored by mesh refinement near the corners of the domain.