# Moving Mesh Methods for Problems with Blow-Up

@article{Budd1996MovingMM, title={Moving Mesh Methods for Problems with Blow-Up}, author={Chris J. Budd and Weizhang Huang and Robert D. Russell}, journal={SIAM J. Sci. Comput.}, year={1996}, volume={17}, pages={305-327} }

In this paper we consider the numerical solution of PDEs with blow-up for which scaling invariance plays a natural role in describing the underlying solution structures. It is a challenging numerical problem to capture the qualitative behaviour in the blow-up region, and the use of nonuniform meshes is essential. We consider moving mesh methods for which the mesh is determined using so-called moving mesh partial differential equations (MMPDEs). Specifically, the underlying PDE and the MMPDE are…

## 207 Citations

Moving Mesh Methods with Applications to Blow-up Problems for PDEs

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This dissertation examines the application of moving mesh methods that are based on the principle of conservation of certain quantities to a number of semi-linear partial differential equations (PDEs), considering the Fisher's equation, Non-linear Schrödinger equation and the Cahn-Allen equation.

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