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… 

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