Moving mesh methods for solving parabolic partial differential equations

作者：Marlow R^*; Hubbard M E; Jimack P K

来源：Computers & Fluids, 2011, 46(1): 353-361.

DOI：10.1016/j.compfluid.2010.11.034

• Moving meshes
• Finite elements
• Moving boundaries
• Parabolic PDEs
• Porous medium equation

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.

• 出版日期2011-7