A moving mesh finite element algorithm for the adaptive solution of time-dependent partial differential equations with moving boundaries
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Publication:2486141
DOI10.1016/j.apnum.2004.09.013zbMath1073.65097OpenAlexW2148256773WikidataQ60501070 ScholiaQ60501070MaRDI QIDQ2486141
Publication date: 5 August 2005
Published in: Applied Numerical Mathematics (Search for Journal in Brave)
Full work available at URL: http://eprints.whiterose.ac.uk/1764/1/jimackp35_BHJ04.pdf
algorithmnumerical examplesStefan problemporous medium equationFinite element methodLagrangian meshesMoving boundariesConservation of massTime-dependent nonlinear diffusion
Nonlinear parabolic equations (35K55) Stefan problems, phase changes, etc. (80A22) Flows in porous media; filtration; seepage (76S05) Finite element methods applied to problems in fluid mechanics (76M10) Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs (65M60) Free boundary problems for PDEs (35R35)
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Cites Work
- Unnamed Item
- Self-adjusting grid methods for one-dimensional hyperbolic conservation laws
- The moving finite element method: Applications to general partial differential equations with multiple large gradients
- Unified approach to simulation on deforming elements with application to phase change problems
- Numerical computation of the free boundary for the two-dimensional Stefan problem by space-time finite elements
- A simple level set method for solving Stefan problems
- Mathematical biology. Vol. 1: An introduction.
- Variational algorithms and pattern formation in dendritic solidification
- Parallel adaptive \(hp\)-refinement techniques for conservation laws
- Level-set-based deformation methods for adaptive grids
- Analysis of an algorithm for generating locally optimal meshes for 𝐿₂ approximation by discontinuous piecewise polynomials
- Geometric Conservation Law and Its Application to Flow Computations on Moving Grids
- Temporal Derivatives in the Finite-Element Method on Continuously Deforming Grids
- A new approach to grid generation
- Numerical Solution of a Diffusion Consumption Problem with a Free Boundary
- Algorithms for Optimal Discontinuous Piecewise Linear and Constant L 2 Fits to Continuous Functions with Adjustable Nodes in One and Two Dimensions
- Moving Mesh Partial Differential Equations (MMPDES) Based on the Equidistribution Principle
- A Moving Mesh Method Based on the Geometric Conservation Law
- Moving Mesh Methods for Problems with Blow-Up
- The solution of two-dimensional free-surface problems using automatic mesh generation
- The geometric integration of scale-invariant ordinary and partial differential equations
- A moving mesh finite element method for the solution of two-dimensional Stefan problems
