Accepted

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

Long Chen

SIAM Journal on Numerical Analysis

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ABSTRACT:

    Finite volume methods are an important class of discretization
    method since the conservation law is locally preserved and the
    capability of discretizing complex geometry domains. However it is
    limited by low order approximation since most finite volume
    methods use piecewise constant or linear function space. 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 a linear finite volume method. Our new
    method is modified from hierarchical basis finite element
    method. Optimal convergence rate in $H^1$-norm of quadratic finite
    volume methods for Poisson equation over two dimensional
    triangular and rectangular grids is obtained and numerical
    examples are provided to show the effective of the method.