Tangential Errors of Tensor Surface Finite Elements
arXiv:2106.01000 · doi:10.1093/imanum/drac015
Abstract
We discretize a tangential tensor field equation using a surface-finite element approach with a penalization term to ensure almost tangentiality. It is natural to measure the quality of such a discretization intrinsically, i.e., to examine the tangential convergence behavior in contrast to the normal behavior. We show optimal order convergence with respect to the tangential quantities in particular for an isogeometric penalization term that is based only on the geometric information of the discrete surface.
arXiv comment44 pages
References in corpus (15)
- Geodesics in Heat
- High order unfitted finite element methods on level set domains using isoparametric mappings
- Incompressible fluid problems on embedded surfaces: Modeling and variational formulations
- Surface free energies for nematic shells
- Higher-order surface FEM for incompressible Navier-Stokes flows on manifolds
- Solving the incompressible surface Navier-Stokes equation by surface finite elements
- A finite element approach for vector- and tensor-valued surface PDEs
- Hydrodynamic Flows on Curved Surfaces: Spectral Numerical Methods for Radial Manifold Shapes
- Orientational order on surfaces - the coupling of topology, geometry, and dynamics
- Analysis of Finite Element Methods for Vector Laplacians on Surfaces
- Finite element discretization methods for velocity-pressure and stream function formulations of surface Stokes equations
- Divergence-free tangential finite element methods for incompressible flows on surfaces
- Approximation of tensor fields on surfaces of arbitrary topology based on local Monge parametrizations
- Dune-CurvedGrid -- A Dune module for surface parametrization
- Higher order Trace Finite Element Methods for the Surface Stokes Equation