Numerical quenching for a semilinear parabolic equation
Abstract
This paper concerns the study of the numerical approximation for the nonlinear parabolic boundary value problem with the source term leading to the quenching in finite time. We find some conditions under which the solution of a semidiscrete form of the above problem quenches in a finite time and estimate its semidiscrete quenching time. We also prove that the semidiscrete quenching time converges to the real one when the mesh size goes to zero. A similar study has been also investigated taking a discrete form of the above problem. Finally, we give some numerical experiments to illustrate our analysis.
First Published Online: 14 Oct 2010
Keywords:
Semidiscretizations, semilinear parabolic equation, quenching, numerical quenching time, convergenceHow to Cite
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Copyright (c) 2008 The Author(s). Published by Vilnius Gediminas Technical University.
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Copyright (c) 2008 The Author(s). Published by Vilnius Gediminas Technical University.
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This work is licensed under a Creative Commons Attribution 4.0 International License.