Abstracts for the Conference on
Grid Adaptivity in Computational PDEs,
Edinburgh, July 96		Next
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Adaptive FEM for reaction-diffusion equations

J Lang (Invited Presentation)

Scientific Computing,
Konrad Zuse Zentrum fuer Informationstechnik Berlin
Heilbronner Str. 10,
D-10711 Berlin-Wilmersdorf, Germany.
e-mail: lang@ZIB-Berlin.DE

Abstract

An integrated time-space adaptive finite element method for solving systems of nonlinear parabolic and elliptic equations in complex geometry is presented. The partial differential system is first discretized in time using singly diagonally linearly implicit Runge-Kutta methods. Local time errors computed by an embedding strategy are used to propose a new time step by a combined P/PI-controller algorithm. An adaptive finite element method on unstructed meshes is subsequently applied for the discretization in space. The local estimates of the finite element solution steering the adaptive mesh refinement are obtained solving local Dirichlet problems with higher accuracy.

The devised method is applied to two-dimensional laminar gaseous combustion, solid-solid alloying reactions and three-dimensional bio-heat transfer equations. It is demonstrated that for such demanding applications the employed error estimations and adaptive strategies generate an efficient and robust algorithm.

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Last modified Fri Jun 21 19:19:14 GB-Eire 1996 (DBD)