Convergence of the discontinuous finite volume method for elliptic problems with minimal regularity

This paper investigates convergence of the discontinuous finite volume method (DFVM) under minimal regularity assumptions on solutions of second order elliptic boundary value problems. Conventional analysis requires the solutions to be in Sobolev spaces H1+s,s>12. Here we assume the solutions are in H1+s,s>0H1+s,s>0 and employ the techniques developed in Gudi (2010) [18] and [20] to derive error estimates in a mesh-dependent energy norm and the L2L2-norm for DFVM. The theoretical estimates are illustrated by numerical results, which include problems with corner singularity and intersecting interfaces.