Higher Order May Be Better or May Not Be Better: Investigations with the FDEM (Finite Difference Element Method)

Authors:
Willi Schönauer;Torsten Adolph
Affiliations:
Rechenzentrum der Universität Karlsruhe, D-76128 Karlsruhe, Germany. schoenauer@rz.uni-karlsruhe.de;Rechenzentrum der Universität Karlsruhe, D-76128 Karlsruhe, Germany
Venue:
Journal of Scientific Computing
Year:
2002

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Abstract

The FDEM program package is a black-box solver for nonlinear systems of elliptic and parabolic PDEs. A FDM of arbitrary consistency order q on an unstructured basic FEM mesh is used. With the difference formula of order q+2 an error estimate is computed. A sophisticated algorithm has been developed to generate reliable difference formulae of order q on an unstructured grid. Completely new is the usage of the error estimate to determine under such general conditions for each node i its individual optimal order q(i) out of the orders 2, 4, 6. This order control tells us that higher order may be better or may not be better, depending on the character of the solution and the used mesh.