Journal
JOURNAL OF COMPUTATIONAL PHYSICS
Volume 176, Issue 1, Pages 205-227Publisher
ACADEMIC PRESS INC ELSEVIER SCIENCE
DOI: 10.1006/jcph.2001.6977
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In this paper, we consider the variable coefficient Poisson equation with Dirichlet boundary conditions on an irregular domain and show that one can obtain second-order accuracy with a rather simple discretization. Moreover, since our discretization matrix is symmetric, it can be inverted rather quickly as opposed to the more complicated nonsymmetric discretization matrices found in other second-order-accurate discretizations of this problem. Multidimensional computational results are presented to demonstrate the second-order accuracy of this numerical method. In addition, we use our approach to formulate a second-order-accurate symmetric implicit time discretization of the heat equation on irregular domains. Then we briefly consider Stefan problems. (C) 2002 Elsevier Science (USA).
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