Inf-sup stability of the trace $\mathbf {P}_2$–$P_1$ Taylor–Hood elements for surface PDEs

DOI10.1090/mcom/3551zbMath1486.65261arXiv1909.02990OpenAlexW2971465021WikidataQ114094320 ScholiaQ114094320MaRDI QIDQ4992223

Arnold Reusken, Alexander Zhiliakov, Maxim A. Olshanskii

Publication date: 7 June 2021

Published in: Mathematics of Computation (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1909.02990

zbMATH Keywords

Taylor-Hood elementsmaterial surfacesfluidic membranestrace finite element methodsurface Stokes problem

Mathematics Subject Classification ID

Error bounds for boundary value problems involving PDEs (65N15) Stokes and related (Oseen, etc.) flows (76D07) Stability and convergence of numerical methods for boundary value problems involving PDEs (65N12) Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs (65N30) Boundary value problems on manifolds (58J32)

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Uses Software

• CutFEM

Cites Work

• Unnamed Item
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• A stable numerical method for the dynamics of fluidic membranes
• Infinite-dimensional dynamical systems in mechanics and physics
• A continuum theory of elastic material surfaces
• Topological methods in hydrodynamics
• Incompressible fluid problems on embedded surfaces: modeling and variational formulations
• A penalty finite element method for a fluid system posed on embedded surface
• A stabilized cut finite element method for partial differential equations on surfaces: the Laplace-Beltrami operator
• An unfitted finite element method, based on Nitsche's method, for elliptic interface problems.
• Theory and practice of finite elements.
• A stabilized cut finite element method for the Darcy problem on surfaces
• Groups of diffeomorphisms and the motion of an incompressible fluid
• Trace finite element methods for PDEs on surfaces
• A Higher Order Finite Element Method for Partial Differential Equations on Surfaces
• Finite Element Methods for Incompressible Flow Problems
• A finite element approach to incompressible two-phase flow on manifolds
• An Adaptive Surface Finite Element Method Based on Volume Meshes
• Iterative Methods for Linear Systems
• CutFEM: Discretizing geometry and partial differential equations
• Energetic variational approaches for incompressible fluid systems on an evolving surface
• A Finite Element Method for Elliptic Equations on Surfaces
• Error estimates for a mixed finite element approximation of the Stokes equations
• Analysis of trace finite element methods for surface partial differential equations
• Mixed and Hybrid Finite Element Methods
• Analysis on Morrey Spaces and Applications to Navier-Stokes and Other Evolution Equations
• An Unfitted Hybrid High-Order Method for Elliptic Interface Problems
• A Finite Element Method for the Surface Stokes Problem
• Analysis of a High-Order Trace Finite Element Method for PDEs on Level Set Surfaces
• Inf-sup stability of geometrically unfitted Stokes finite elements
• Erratum: The Interplay of Curvature and Vortices in Flow on Curved Surfaces
• Trace finite element methods for surface vector-Laplace equations
• A Divergence-Conforming Finite Element Method for the Surface Stokes Equation
• The Interplay of Curvature and Vortices in Flow on Curved Surfaces
• Cut finite element methods for partial differential equations on embedded manifolds of arbitrary codimensions
• Stream function formulation of surface Stokes equations
• Analysis of finite element methods for vector Laplacians on surfaces
• Navier-Stokes equations on Lipschitz domains in Riemannian manifolds.

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