A Novel Arbitrary Lagrangian–Eulerian Finite Element Method for a Mixed Parabolic Problem in a Moving Domain
Journal of Scientific Computing
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In this paper, a novel arbitrary Lagrangian–Eulerian (ALE) mapping, thus a novel ALE-mixed finite element method (FEM), is developed and analyzed for a type of mixed parabolic equations in a moving domain. By means of a specific stabilization technique, the mixed finite element of a stable Stokes-pair is utilized to discretize this problem on the ALE description, and, stability and a nearly optimal convergence results are obtained for both semi- and fully discrete ALE finite element approximations. Numerical experiments are carried out to validate all theoretical results. The developed novel ALE–FEM can be also similarly extended to a transient porous (Darcy’s) fluid flow problem in a moving domain as well as to Stokes/Darcy- or Stokes/Biot moving interface problem in the future.
Mixed Parabolic Moving Domain Problem; Arbitrary Lagrangian–Eulerian (ALE) Mapping; Piola Transformation; Mixed Finite Element; Optimal Error Estimates; Stability
Mathematics | Physical Sciences and Mathematics
A Novel Arbitrary Lagrangian–Eulerian Finite Element Method for a Mixed Parabolic Problem in a Moving Domain.
Journal of Scientific Computing, 85