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Explorations and Expectations of Equidistribution Adaptations for Nonlinear Quenching Problems

Published online by Cambridge University Press:  03 June 2015

Matthew A. Beauregard  and
Qin Sheng
Matthew A. Beauregard*
Affiliation:
Department of Mathematics, Baylor University, TX 76798-7328, USA
Qin Sheng*
Affiliation:
Department of Mathematics, Baylor University, TX 76798-7328, USA
*
Corresponding author. Email: Matthew_Beauregard@baylor.edu
Email: Qin_Sheng@baylor.edu
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Abstract

Finite difference computations that involve spatial adaptation commonly employ an equidistribution principle. In these cases, a new mesh is constructed such that a given monitor function is equidistributed in some sense. Typical choices of the monitor function involve the solution or one of its many derivatives. This straightforward concept has proven to be extremely effective and practical. However, selections of core monitoring functions are often challenging and crucial to the computational success. This paper concerns six different designs of the monitoring function that targets a highly nonlinear partial differential equation that exhibits both quenching-type and degeneracy singularities. While the first four monitoring strategies are within the so-called primitive regime, the rest belong to a later category of the modified type, which requires the priori knowledge of certain important quenching solution characteristics. Simulated examples are given to illustrate our study and conclusions.

Keywords

65K2065M5035K65Degeneracyquenching singularityadaptive difference methodarc-lengthmonitoring functionsplitting method
Type
Research Article
Information
Advances in Applied Mathematics and Mechanics , Volume 5 , Special Issue 4 , August 2013 , pp. 407 - 422
Copyright
Copyright © Global-Science Press 2013

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