Unified Analysis of Finite Volume Methods for Second Order Elliptic Problems

Abstract

We establish a general framework for analyzing the class of finite volume methods which employ continuous or totally discontinuous trial functions and piecewise constant test functions. Under the framework, optimal order convergence in the $H^1$ and $L^2$ norms can be obtained in a natural and systematic way for classical finite volume methods and new finite volume methods such as discontinuous finite volume methods applied to second order elliptic problems.

Locations

• SIAM Journal on Numerical Analysis - View
• ScholarWorks - BGSU (Bowling Green State University) - View - PDF