Convergence analysis of an upwind finite volume element method with Crouzeix-Raviart element for non-selfadjoint and indefinite problems

Abstract

In this paper we construct an upwind finite volume element scheme based on the Crouzeix-Raviart nonconforming element for non-selfadjoint elliptic problems. These problems often appear in dealing with flow in porous media. We establish the optimal order H¹-norm error estimate. We also give the uniform convergence under minimal elliptic regularity assumption

Keywords

Finite volume element (FVE) method / upwind method / Crouzeix-Raviart element / optimal order convergence / uniform convergence / convection-diffusion problem

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