Point-distributed algorithms on locally refined grids for second order elliptic equations

Authors:
Richard E. Ewing;Jian Shen;Junping Wang
Affiliations:
Institute for Scientific Computation, 612 John R. Blocker Building, Texas A&M University, 3404 TAMU, College Station, Texas;Lockheed Martin;Mathematics Department, University of Wyoming, Box 3036, Laramie, Wyoming
Venue:
Scientific computing and applications
Year:
2001

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Abstract

A discretization scheme, which relates the mixed finite element method with cell-centered finite difference and finite volume element methods, is proposed for second-order elliptic equations on rectangular domains with locally refined composite grids. Optimal order error estimates and superconvergence results are established, both in L2 and pointwise along special Gauss-line loci. These error estimates hold for discontinuous piecewise constant conductivity under some special assumptions about solutions.