A Patch/Subdomain Iteration Framework and Algorithm Class for Error Indicator and Mesh Reliability Calculations

A patch iteration approach and class of algorithms are described for inexpensively enhancing error indicators based on residuals and local boundary-value problems. The scheme is applicable to finite element, finite volume, finite difference and similar discretization schemes. It exploits ideas from multicolor/multilevel iterative relaxation at the patch level and more generally overlapping Schwarz subdomain iteration concepts. The scheme can be 'retrofitted' to existing serial or parallel codes to enhance local indicators, reduce pollution effects, yield improved stopping criteria for refinement or even simply to assess the reliability of a Computation on a given grid. Extrapolation techniques for further enhancing the patch iteration indicator and other extensions such as application to the adjoint solve step for dual formulations are also described. Copyright (C) 2007 John Wiley & Sons, Ltd.