Biquartic Finite Volume Element Method Based on Lobatto-Guass Structure

Abstract

In this paper, a biquartic finite volume element method based on Lobatto-Guass structure is presented for variable coefficient elliptic equation on rectangular partition. Not only the optimal $H^1$ and $L^2$ error estimates but also some superconvergent properties are available and could be proved for this method. The numerical results obtained by this finite volume element scheme confirm the validity of the theoretical analysis and the effectiveness of this method.