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Scale-invariant moving finite elements for nonlinear partial differential equations in two dimensions

By M.J. Baines, M.E. Hubbard, P.K. Jimack and A.C. Jones


A scale-invariant moving finite element method is proposed for the adaptive solution of nonlinear partial differential equations. The mesh movement is based on a finite element discretisation of a scale-invariant conservation principle incorporating a monitor function, while the time discretisation of the resulting system of ordinary differential equations is carried out using a scale-invariant time-stepping which yields uniform local accuracy in time.\ud \ud The accuracy and reliability of the algorithm are successfully tested against exact self-similar solutions where available, and otherwise against a state-of-the-art h-refinement scheme for solutions of a two-dimensional porous medium equation problem with a moving boundary. The monitor functions used are the dependent variable and a monitor related to the surface area of the solution manifold

Publisher: Elsevier B.V.
Year: 2006
OAI identifier: oai:eprints.whiterose.ac.uk:1784

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