A moving mesh finite element algorithm for the adaptive solution of time-dependent partial differential equations with moving boundaries

Authors:
M. J. Baines;M. E. Hubbard;P. K. Jimack
Affiliations:
Department of Mathematics, The University of Reading, UK;School of Computing, University of Leeds, UK;School of Computing, University of Leeds, UK
Venue:
Applied Numerical Mathematics - Selected papers from the 16th Chemnitz finite element symposium 2003
Year:
2005

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Abstract

A moving mesh finite element algorithm is proposed for the adaptive solution of nonlinear diffusion equations with moving boundaries in one and two dimensions. The moving mesh equations are based upon conserving a local proportion, within each patch of finite elements, of the total "mass" that is present in the projected initial data. The accuracy of the algorithm is carefully assessed through quantitative comparison with known similarity solutions, and its robustness is tested on more general problems.Applications are shown to a variety of problems involving time-dependent partial differential equations with moving boundaries. Problems which conserve mass, such as the porous medium equation and a fourth order non-linear diffusion problem, can be treated by a simplified form of the method, while problems which do not conserve mass require the full theory.