Error analysis of higher order trace finite element methods for the surface Stokes equations
arXiv:2003.06972
Abstract
The paper studies a higher order unfitted finite element method for the Stokes system posed on a surface in three-dimensional space. The method employs generalized Taylor-Hood finite element pairs on tetrahedral bulk mesh to discretize the Stokes system on embedded surface. Stability and optimal order convergence results are proved. The proofs include a complete quantification of geometric errors stemming from approximate parametric representation of the surface. Numerical experiments include formal convergence studies and an example of the Kelvin-Helmholtz instability problem on the unit sphere.
arXiv comment28 pages, 3 figures
References in corpus (9)
- High order unfitted finite element methods on level set domains using isoparametric mappings
- Incompressible fluid problems on embedded surfaces: Modeling and variational formulations
- Higher-order surface FEM for incompressible Navier-Stokes flows on manifolds
- Meshfree Methods on Manifolds for Hydrodynamic Flows on Curved Surfaces: A Generalized Moving Least-Squares (GMLS) Approach
- Analysis of Finite Element Methods for Vector Laplacians on Surfaces
- On reference solutions and the sensitivity of the 2D Kelvin-Helmholtz instability problem
- Approximation of tensor fields on surfaces of arbitrary topology based on local Monge parametrizations
- Inf-sup stability of the trace P2-P1 Taylor-Hood elements for surface PDEs
- Higher order Trace Finite Element Methods for the Surface Stokes Equation