Moving mesh methods for solving parabolic partial differential equations

DOI10.1016/j.compfluid.2010.11.034zbMath1278.65154OpenAlexW2146813411MaRDI QIDQ536762

Peter K. Jimack, Randall S. Marlow, Matthew Hubbard

Publication date: 19 May 2011

Published in: Computers and Fluids (Search for Journal in Brave)

Full work available at URL: http://etheses.whiterose.ac.uk/1528/1/marlow.pdf

zbMATH Keywords

finite elementsporous medium equationmoving boundariesparabolic PDEsmoving meshes

Mathematics Subject Classification ID

Flows in porous media; filtration; seepage (76S05) Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs (65M60) Mesh generation, refinement, and adaptive methods for the numerical solution of initial value and initial-boundary value problems involving PDEs (65M50)

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A numerical method based on the moving mesh for the solving of a mathematical model of the avascular tumor growth ⋮ A velocity-based moving mesh virtual element method ⋮ Adaptive numerical method for Burgers-type nonlinear equations

Uses Software

• SUNDIALS
• MOVCOL

Cites Work

• MOVCOL
• Mathematical biology. Vol. 2: Spatial models and biomedical applications.
• A moving mesh finite element algorithm for the adaptive solution of time-dependent partial differential equations with moving boundaries
• Scale-invariant moving finite elements for nonlinear partial differential equations in two dimensions
• Adaptivity with moving grids
• A Local Convergence Theory for Combined Inexact-Newton/Finite-Difference Projection Methods
• Parabolic Monge–Ampère methods for blow-up problems in several spatial dimensions

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