Abstracts for the Conference on
Grid Adaptivity in Computational PDEs,
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The efficient generation of simple two-dimensional adaptive grids

J A Mackenzie

Department of Mathematics
University of Strathclyde
Livingstone Tower
26 Richmond Street
Glasgow, Scotland

Abstract

We present an efficient adaptive procedure for solving steady partial differential equations based on the simple two-dimensional quadrilateral grid generator. The mesh equations are derived using an equidistribution principle and are discretised in the physical domain. This allows the application of the adaptive grid generator to finite element and finite volume methods. To efficiently solve the nonlinear algebraic equations describing the adapted grid, we propose an alternating line Gauss-Seidel relaxation procedure. The beneficial effect of adaptive grids is demonstrated by coupling the grid generator to finite volume and finite difference approximations of advection and advection-diffusion test problems. For some examples the proposed method is shown to be $50$ times more efficient than previously used solution procedures.
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Last modified Fri Jun 21 19:19:14 GB-Eire 1996 (DBD)