Consistent Dirichlet boundary conditions for numerical solution of moving boundary problems

Authors:
M. E. Hubbard;M. J. Baines;P. K. Jimack
Affiliations:
University of Leeds, School of Computing, Leeds, UK;The University of Reading, Department of Mathematics, Reading, UK;University of Leeds, School of Computing, Leeds, UK
Venue:
Applied Numerical Mathematics
Year:
2009

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Abstract

We consider the imposition of Dirichlet boundary conditions in the finite element modelling of moving boundary problems in one and two dimensions for which the total mass is prescribed. A modification of the standard linear finite element test space allows the boundary conditions to be imposed strongly whilst simultaneously conserving a discrete mass. The validity of the technique is assessed for a specific moving mesh finite element method, although the approach is more general. Numerical comparisons are carried out for mass-conserving solutions of the porous medium equation with Dirichlet boundary conditions and for a moving boundary problem with a source term and time-varying mass.