High Order Finite Volume Methods for Second Order Elliptic equations
Dr. Long Chen
Department of Mathematics
University of California, Irvine
Abstract
Finite volume methods are an important class of discretization
methods 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 talk, 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 a hierarchical basis finite element method.