Title

A Novel Arbitrary Lagrangian–Eulerian Finite Element Method for a Parabolic/Mixed Parabolic Moving Interface Problem

Document Type

Article

Publication Date

8-1-2020

Publication Title

Journal of Computational and Applied Mathematics

Volume

383

First page number:

1

Last page number:

33

Abstract

In this paper, a monolithic arbitrary Lagrangian–Eulerian (ALE)-finite element method (FEM) is developed based upon a novel ALE mapping for a type of parabolic/mixed parabolic moving interface problem with jump coefficients. A stable Stokes-pair mixed FEM within a specific stabilization technique and a novel ALE time-difference scheme are developed to discretize this interface problem in both semi- and fully discrete fashion, for which the stability and error estimate analyses are conducted in the ALE frame. Numerical experiments are carried out to validate all theoretical results in different cases. The developed novel ALE-FEM can be extended to a moving interface problem that involves the pore fluid (Darcy) equation or Biot’s model in the future.

Keywords

Parabolic/mixed Parabolic Moving Interface problem; Arbitrary Lagrangian–Eulerian (ALE) Mapping; Piola Transformation; Mixed Finite Element Method; Error Estimates; Stability

Disciplines

Mathematics | Physical Sciences and Mathematics

Language

English

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