A novel arbitrary Lagrangian-Eulerian finite element method for a parabolic/mixed parabolic moving interface problem

DOI10.1016/j.cam.2020.113125zbMath1479.65007OpenAlexW3046866282MaRDI QIDQ2199780

Rihui Lan, Pengtao Sun

Publication date: 14 September 2020

Published in: Journal of Computational and Applied Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.cam.2020.113125

zbMATH Keywords

stabilityerror estimatesmixed finite element methodPiola transformationarbitrary Lagrangian-Eulerian (ALE) mappingparabolic/mixed parabolic moving interface problem

Mathematics Subject Classification ID

Finite element methods applied to problems in solid mechanics (74S05) Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs (65N30) Finite difference methods for initial value and initial-boundary value problems involving PDEs (65M06) Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs (65M12) 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) Error bounds for initial value and initial-boundary value problems involving PDEs (65M15)

Related Items (4)

Multiscale and monolithic arbitrary Lagrangian-Eulerian finite element method for a hemodynamic fluid-structure interaction problem involving aneurysms ⋮ An energy diminishing arbitrary Lagrangian-Eulerian finite element method for two-phase Navier-Stokes flow ⋮ Meshfree methods for nonlinear equilibrium radiation diffusion equation with jump coefficient ⋮ New finite volume element methods in the ALE framework for time-dependent convection-diffusion problems in moving domains

Cites Work

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• Finite element analysis of an arbitrary Lagrangian-Eulerian method for Stokes/parabolic moving interface problem with jump coefficients
• A stable finite element for the Stokes equations
• Lagrangian-Eulerian finite element formulation for incompressible viscous flows
• Time domain fundamental solution to Biot's complete equations of dynamic poroelasticity. II: Three-dimensional solution
• Convergence of a finite element/ALE method for the Stokes equations in a domain depending on time
• Stability and geometric conservation laws for ALE formulations
• A splitting positive definite mixed element method for miscible displacement of compressible flow in porous media
• Efficient Assembly of $H(\mathrm{div})$ and $H(\mathrm{curl})$ Conforming Finite Elements
• An arbitrary lagrangian-eulerian velocity potential formulation for fluid-structure interaction
• Theory of Elasticity and Consolidation for a Porous Anisotropic Solid
• MIXED FINITE ELEMENT METHODS WITH CONTINUOUS STRESSES
• Mixed Finite Element Methods and Applications
• Advanced Transport Phenomena
• An arbitrary Lagrangian-Eulerian computing method for all flow speeds

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