Numerical Approximation of Large Contrast Problems with the Unfitted Nitsche Method

DOI10.1007/978-3-642-23914-4_4zbMath1248.65121OpenAlexW2267060181MaRDI QIDQ2902954

Erik Burman, Paolo Zunino

Publication date: 23 August 2012

Published in: Lecture Notes in Computational Science and Engineering (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/978-3-642-23914-4_4

zbMATH Keywords

finite element methodPoisson equationNitsche's methodsecond order elliptic problem

Mathematics Subject Classification ID

Boundary value problems for second-order elliptic equations (35J25) Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs (65N30) Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation (35J05)

Related Items

A consistent computational approach for general fluid-poroelasticity-structure-contact interaction problems, Nitsche's method for finite deformation thermomechanical contact problems, A finite element method for high-contrast interface problems with error estimates independent of contrast, Interface-penalty finite element methods for interface problems in \(H^1\), \(\boldsymbol{H} (\mathbf{curl})\), and \(\boldsymbol{H} (\operatorname{div})\), A two-level additive Schwarz preconditioner for the Nitsche extended finite element approximation of elliptic interface problems, High-order enforcement of jumps conditions between compressible viscous phases: an extended interior penalty discontinuous Galerkin method for sharp interface simulation, A conforming virtual element method based on unfitted meshes for the elliptic interface problem, Unfitted finite element methods for the heat conduction in composite media with contact resistance, An extended algebraic variational multiscale-multigrid-multifractal method (XAVM\(^4\)) for large-eddy simulation of turbulent two-phase flow, Stabilized Cut Discontinuous Galerkin Methods for Advection-Reaction Problems, Analysis of backward Euler/extended finite element discretization of parabolic problems with moving interfaces, Robust and scalable \(h\)-adaptive aggregated unfitted finite elements for interface elliptic problems, A CutFEM method for two-phase flow problems, A Nonconforming Nitsche's Extended Finite Element Method for Elliptic Interface Problems, Optimal preconditioners for Nitsche-XFEM discretizations of interface problems, Deep Nitsche Method: Deep Ritz Method with Essential Boundary Conditions, Multimesh finite elements with flexible mesh sizes, An unfitted interface penalty method for the numerical approximation of contrast problems, Recent developments in variational multiscale methods for large-eddy simulation of turbulent flow, Efficient multigrid solution of elliptic interface problems using viscosity-upwinded local discontinuous Galerkin methods, A Multigrid Method for Unfitted Finite Element Discretizations of Elliptic Interface Problems, On the accuracy of finite element approximations to a class of interface problems, A Minimal Stabilization Procedure for Isogeometric Methods on Trimmed Geometries, Numerical solvers for a poromechanic problem with a moving boundary, An unfitted interface penalty finite element method for elliptic interface problems, Higher-order finite element methods for elliptic problems with interfaces

Cites Work

• Unnamed Item
• Unnamed Item
• Fictitious domain finite element methods using cut elements. II: A stabilized Nitsche method
• Ghost penalty
• Discontinuous Galerkin methods based on weighted interior penalties for second order PDEs with non-smooth coefficients
• Fictitious domain finite element methods using cut elements. I: A stabilized Lagrange multiplier method
• An unfitted interface penalty method for the numerical approximation of contrast problems
• An extended pressure finite element space for two-phase incompressible flows with surface tension
• Analysis of an efficient finite element method for embedded interface problems
• The boundary value problems of mathematical physics. Transl. from the Russian by Jack Lohwater
• Boundary subspaces for the finite element method with Lagrange multipliers
• Boundary Lagrange multipliers in finite element methods: Error analysis in natural norms
• The finite element method with Lagrange multipliers on the boundary: Circumventing the Babuška-Brezzi condition
• On the coupling of hyperbolic and parabolic systems: Analytical and numerical approach
• A discontinuous \(hp\) finite element method for diffusion problems
• Finite element approximation of the Dirichlet problem using the boundary penalty method
• An unfitted finite element method, based on Nitsche's method, for elliptic interface problems.
• Error analysis of a fictitious domain method applied to a Dirichlet problem
• On some techniques for approximating boundary conditions in the finite element method
• A finite element method for the simulation of strong and weak discontinuities in solid mechanics
• The finite element method with Lagrangian multipliers
• Nitsche’s method for general boundary conditions
• A Finite Element Method Based on Weighted Interior Penalties for Heterogeneous Incompressible Flows
• Continuous interior penalty $hp$-finite element methods for advection and advection-diffusion equations
• Imposing Dirichlet boundary conditions in the extended finite element method
• Continuous Interior Penalty Finite Element Method for Oseen's Equations
• An efficient finite element method for embedded interface problems
• Numerical Analysis of a Finite Element/Volume Penalty Method
• A New Fictitious Domain Approach Inspired by the Extended Finite Element Method
• An embedded Dirichlet formulation for 3D continua
• Nitsche's method for interface problems in computa-tional mechanics
• A discontinuous Galerkin method with weighted averages for advection-diffusion equations with locally small and anisotropic diffusivity
• Local Stability Conditions for the Babuska Method of Lagrange Multipliers
• The Finite Element Method with Lagrange Multipliers for Domains with Corners
• The Lagrange Multiplier Method for Dirichlet's Problem
• An Interior Penalty Finite Element Method with Discontinuous Elements
• The Finite Element Method with Penalty
• A finite element method for domain decomposition with non-matching grids
• Raytcho Lazarov - 60
• A Priori Error Estimates for Finite Element Methods Based on Discontinuous Approximation Spaces for Elliptic Problems
• Unified Analysis of Discontinuous Galerkin Methods for Elliptic Problems
• Approximate imposition of boundary conditions in immersed boundary methods
• The Mathematical Theory of Finite Element Methods
• A Unified Analysis for Conforming and Nonconforming Stabilized Finite Element Methods Using Interior Penalty
• A Domain Decomposition Method Based on Weighted Interior Penalties for Advection‐Diffusion‐Reaction Problems
• An extended finite element method for modeling crack growth with frictional contact.
• Analysis of an extended pressure finite element space for two-phase incompressible flows