A New Class of High Order Finite Volume Methods for Second Order Elliptic Equations

In the numerical simulation of many practical problems in physics and engineering, finite volume methods are an important and popular class of discretization methods due to the local conservation and the capability of discretizing domains with complex geometry. However they are limited by low order approximation since most existing finite volume methods use piecewise constant or linear function space to approximate the solution. In this paper, a new class of high order finite volume methods for second order elliptic equations is developed by combining high order finite element methods and linear finite volume methods. Optimal convergence rate in H1-norm for our new quadratic finite volume methods over two dimensional triangular or rectangular grids is obtained. Key words. finite element, finite volume, discretization, error estimates, high order methods AMS subject classifications. 65N10, 65N30

• Type: Journal
• Year: 2010
• Where: SIAMNUM
• Authors: Long Chen
• Keywords: Finite Volume, Finite Volume Methods, Order Finite Volume, SIAMNUM 2010