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On the Solution of Convection-Diffusion Boundary Value Problems Using Equidistributed Grids

Budd, C. J. and Koomullil, G. P. and Stuart, A. M. (1998) On the Solution of Convection-Diffusion Boundary Value Problems Using Equidistributed Grids. SIAM Journal on Scientific Computing, 20 (2). pp. 591-618. ISSN 1064-8275.

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The effect of using grid adaptation on the numerical solution of model convection-diffusion equations with a conservation form is studied. The grid adaptation technique studied is based on moving a fixed number of mesh points to equidistribute a generalization of the arc-length of the solution. In particular, a parameter-dependent monitor function is introduced which incorporates fixed meshes, approximate arc-length equidistribution, and equidistribution of the absolute value of the solution, in a single framework. Thus the resulting numerical method is a coupled nonlinear system of equations for the mesh spacings and the nodal values. A class of singularly perturbed problems, including Burgers's equation in the limit of small viscosity, is studied. Singular perturbation and bifurcation techniques are used to analyze the solution of the discretized equations, and numerical results are compared with the results from the analysis. Computation of the bifurcation diagram of the system is performed numerically using a continuation method and the results are used to illustrate the theory. It is shown that equidistribution does not remove spurious solutions present on a fixed mesh and that, furthermore, the spurious solutions can be stable for an appropriate moving mesh method.

Item Type:Article
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Additional Information:© 1998 Society for Industrial and Applied Mathematics. Received by the editors January 20, 1995; accepted for publication (in revised form) January 22, 1997; published electronically September 10, 1998.
Subject Keywords:convection-diffusion equations, mesh adaptation, equidistribution, continuation
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Other Numbering System NameOther Numbering System ID
Andrew StuartJ38
Classification Code:AMS subject classifications: 65M20, 65M50, 65N50, 35B40
Record Number:CaltechAUTHORS:20170612-143618623
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Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:78124
Deposited By: Tony Diaz
Deposited On:12 Jun 2017 22:00
Last Modified:22 Aug 2017 00:47

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