Efficient computational methods for singular free boundary problems using smoothing variable substitutions

[摘要] We study a class of singular free boundary problems for the degenerate m-Laplacian. Taking into account the behavior of the solution in the neighborhood of the singular points, a variable substitution is introduced, which makes the solution smooth in all the domain. Then, a standard finite difference scheme is used to discretize the problem. The numerical results suggest that in this way the second order convergence of the finite difference scheme is recovered, in spite of the singularities. (C) 2011 Elsevier B.V. All rights reserved.

[发布日期] 2012-06-01

[效力级别]  Proceedings Paper

[关键词] m-Laplacian;Singular Cauchy problem;Singular free boundary problem;Finite difference method;Smoothing variable substitution