Petrov-Galerkin Finite Volumes

TL;DR

This paper introduces a Petrov-Galerkin finite volume method for elliptic problems in two dimensions, utilizing dual Raviart-Thomas basis functions to improve the formulation.

Contribution

It presents a novel finite volume approach based on Petrov-Galerkin mixed finite elements with dual Raviart-Thomas basis, enhancing existing methods.

Findings

Demonstrates the effectiveness of the proposed method for elliptic problems.

Provides theoretical analysis of stability and convergence.

Shows potential for improved accuracy over traditional finite volume methods.

Abstract

For an elliptic problem with two space dimensions, we propose to formulate the finite volume method with the help of Petrov-Galerkin mixed finite elementsthat are based on the building of a dual Raviart-Thomas basis.