Moving mesh methods for solving parabolic partial differential equations |
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Authors: | R Marlow ME Hubbard PK Jimack |
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Affiliation: | a School of Computing, University of Leeds, Leeds LS2 9JT, UK |
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Abstract: | A new adaptive method is described for solving nonlinear parabolic partial differential equations with moving boundaries, using a moving mesh with continuous finite elements. The evolution of the mesh within the interior of the spatial domain is based upon conserving the distribution of a chosen monitor function across the domain throughout time, where the initial distribution is selected based upon the given initial data. The mesh movement at the boundary is governed by a second monitor function, which may or may not be the same as that used to drive the interior mesh movement. The method is described in detail and a selection of computational examples are presented using different monitor functions applied to the porous medium equation (PME) in one and two space dimensions. |
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Keywords: | Moving meshes Finite elements Moving boundaries Parabolic PDEs Porous medium equation |
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