An adaptive discontinuous finite volume method for elliptic problems

An adaptive discontinuous finite volume method is developed and analyzed in this paper. We prove that the adaptive procedure achieves guaranteed error reduction in a mesh-dependent energy norm and has a linear convergence rate. Numerical results are also presented to illustrate the theoretical analysis.

► An adaptive discontinuous finite volume method (DFVM) is developed.
► The adaptive DFVM achieves guaranteed error reduction.
► The adaptive DFVM is asymptotically optimal as nonlinear approximation.