Consistent Dirichlet Boundary Conditions for Numerical Solution of Moving Boundary Problems

Hubbard, M. E., Baines, M. J. and Jimack, P. K. (2009) Consistent Dirichlet Boundary Conditions for Numerical Solution of Moving Boundary Problems. Applied Numerical Mathematics, 59 (6). 1337-1353 . ISSN 0168-9274 doi: 10.1016/j.apnum.2008.08.002

Abstract/Summary

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.

Item Type	Article
URI	https://reading-clone.eprints-hosting.org/id/eprint/1196
Item Type	Article
Refereed	Yes
Divisions	Science > School of Mathematical, Physical and Computational Sciences > Department of Mathematics and Statistics
Uncontrolled Keywords	Finite elements; Dirichlet boundary conditions; Moving boundary problems; Mass conservation
Publisher	Elsevier
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