A new unfitted stabilized Nitsche's finite element method for Stokes interface problems

DOI10.1016/j.camwa.2015.05.024zbMath1443.65376OpenAlexW612415119MaRDI QIDQ2006225

Jinru Chen, Qiuliang Wang

Publication date: 8 October 2020

Published in: Computers \& Mathematics with Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.camwa.2015.05.024

zbMATH Keywords

stabilized finite element methodNitsche's methodStokes interface problemsunfitted interface method

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)

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Cites Work

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• Ghost penalty
• A Nitsche extended finite element method for incompressible elasticity with discontinuous modulus of elasticity
• An unfitted interface penalty method for the numerical approximation of contrast problems
• A stabilized Nitsche overlapping mesh method for the Stokes problem
• A new stabilized finite element method for the transient Navier-Stokes equations
• A stable finite element for the Stokes equations
• On a resolvent estimate of the interface problem for the Stokes system in a bounded domain
• An unfitted finite element method, based on Nitsche's method, for elliptic interface problems.
• Theory and practice of finite elements.
• Stabilized extended finite elements for the approximation of saddle point problems with unfitted interfaces
• First order system least squares method for the interface problem of the Stokes equations
• A stabilized finite element method based on two local Gauss integrations for the Stokes equations
• A finite element method for the simulation of strong and weak discontinuities in solid mechanics
• Analysis of a Stokes interface problem
• A cut finite element method for a Stokes interface problem
• Über ein Variationsprinzip zur Lösung von Dirichlet-Problemen bei Verwendung von Teilräumen, die keinen Randbedingungen unterworfen sind. (On a variational principle for solving Dirichlet problems less boundary conditions using subspaces)
• Nitsche’s method for general boundary conditions
• Error estimates for a mixed finite element approximation of the Stokes equations
• Finite Element Methods for Navier-Stokes Equations
• The Immersed Interface Method for Elliptic Equations with Discontinuous Coefficients and Singular Sources
• Immersed Interface Methods for Stokes Flow with Elastic Boundaries or Surface Tension
• Unified Analysis of Discontinuous Galerkin Methods for Elliptic Problems
• A stabilized finite element method for the Stokes problem based on polynomial pressure projections
• The Mathematical Theory of Finite Element Methods
• Stabilization of Low-order Mixed Finite Elements for the Stokes Equations
• The immersed interface method for the Navier-Stokes equations with singular forces
• Analysis of an extended pressure finite element space for two-phase incompressible flows