On balanced moving mesh methods

• Autores: Joan Remski, Jingyan Zhang, Qiang Du
• Localización: Journal of computational and applied mathematics, ISSN 0377-0427, Vol. 265, Nº 1, 2014, págs. 255-263
• Idioma: inglés
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• Resumen

  • Moving mesh methods are a widely used approach in the numerical solution of PDEs where the original PDEs are transformed from a physical domain to a computational domain. The objective is to utilize a uniform mesh in the computational domain to get a non-uniform physical mesh that better captures the behavior of the solution. The movement of the physical mesh points can be governed by a moving mesh PDE associated with a corresponding monitor function and both the original PDEs and the moving mesh PDEs must be solved simultaneously. The motivation for this paper is to study a balanced moving mesh method, where the aim is to strike a balance between the properties of the solution of the original PDE and that of the moving mesh PDE. We focus on particular choices of the monitor function that give both a well-behaved mesh transformation and a well-behaved solution in the computational domain. Both theoretical analysis and numerical experiments are presented as illustrations.