Finite Volume Scheme for Solving Elliptic Boundary Value Problems on Composite211 Grids

摘要

The authors present a finite volume scheme for solving elliptic boundary value211u001eproblems with solutions that have one or a few small regions with high activity. 211u001eThe scheme results from combining the local defect correction method (LDC) with 211u001estandard finite volume discretizations on a global coarse and on local fine 211u001euniform grids. The iterative discretization method that is obtained in this way 211u001eyields a discrete approximation of the continuous solution on a composite grid. 211u001eFor the LDC method in its standard form, the discrete conservation property, 211u001ewhich is one of the main attractive features of a finite volume method, is lost 211u001efor the composite grid approximation. For the modified LDC method the authors 211u001epresent here, discrete conservation holds for the composite grid solution too.