Abstracts for the Conference on
Grid Adaptivity in Computational PDEs,
Edinburgh, July 96		Next
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A user-oriented insight into the realm of adaptive grid methods for partial differential equations in one space dimension

W E Schiesser¹ , P Saucez & A Vande Wouwer

¹ Computer Science and Engineering,
Lehigh University, USA.

Abstract

Although the use of adaptive grid methods in one spatial dimension is now basically well understood and research is mainly devoted to problems in higher spatial dimensions, only a few methods are available yet in the form of library components of MOL packages and it may still be difficult for the user to find out a path through the ''jungle'' of methods published in the literature.

This study is aimed at bringing together ideas and algorithms which have been proposed over the last fifteen years to adaptively solve one-dimensional partial differential equations in space and time. We examine a number of adaptive grid codes including local refinement algorithms, moving grid algorithms, and ''hybrid'' algorithms. Different approaches for the grid placement are considered, i.e., simultaneous, alternate or periodic node movement. We illustrate and compare the use of the several methods with the numerical solution of a number of test problems taken in science and engineering (e.g., Burgers equation, CSE, KdVE, flame propagation model,...). From the user point of view, we address important questions concerning the accuracy, temporal performance, ease of use, and simplicity of implementation.

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