Gradient recovery for elliptic interface problem. III: Nitsche's method

DOI10.1016/j.jcp.2017.11.031zbMath1380.65368arXiv1705.03617OpenAlexW2613740454MaRDI QIDQ1701053

Hailong Guo, Xu Yang

Publication date: 22 February 2018

Published in: Journal of Computational Physics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1705.03617

zbMATH Keywords

superconvergencegradient recoveryNitsche's methodelliptic interface problempolynomial preserving recovery

Mathematics Subject Classification ID

Boundary value problems for second-order elliptic equations (35J25) Error bounds for boundary value problems involving PDEs (65N15) Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs (65N30) PDEs with low regular coefficients and/or low regular data (35R05)

Related Items (6)

Enriched gradient recovery for interface solutions of the Poisson-Boltzmann equation ⋮ Deep Unfitted Nitsche Method for Elliptic Interface Problems ⋮ Unfitted Nitsche's method for computing band structures of phononic crystals with periodic inclusions ⋮ Gradient Recovery for Elliptic Interface Problem: I. Body-Fitted Mesh ⋮ Unfitted Nitsche's method for computing wave modes in topological materials ⋮ Local ultraconvergence of high order finite element method by interpolation postprocessing technique for elliptic problems with constant coefficients

Uses Software

• FEAPpv
• CutFEM

Cites Work

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• Weak Galerkin methods for second order elliptic interface problems
• A uniformly well-conditioned, unfitted Nitsche method for interface problems
• Fictitious domain finite element methods using cut elements. II: A stabilized Nitsche method
• A weak formulation for solving elliptic interface problems without body fitted grid
• A symmetric and consistent immersed finite element method for interface problems
• Gradient recovery for the Crouzeix-Raviart element
• An interface-fitted adaptive mesh method for elliptic problems and its application in free interface problems with surface tension
• A Nitsche extended finite element method for incompressible elasticity with discontinuous modulus of elasticity
• A finite element method for interface problems in domains with smooth boundaries and interfaces
• A robust Nitsche's formulation for interface problems
• A numerical method for solving variable coefficient elliptic equation with interfaces
• An immersed linear finite element method with interface flux capturing recovery
• Removing the cell resonance error in the multiscale finite element method via a Petrov-Galerkin formulation
• On the fictitious-domain and interpolation formulations of the matched interface and boundary (MIB) method
• A second order virtual node method for elliptic problems with interfaces and irregular domains
• Numerical analysis of blood flow in the heart
• The immersed interface method using a finite element formulation
• Finite element methods and their convergence for elliptic and parabolic interface problems
• New Cartesian grid methods for interface problems using the finite element formulation
• Accurate gradient computations at interfaces using finite element methods
• A new weak Galerkin finite element method for elliptic interface problems
• A review of level-set methods and some recent applications
• Polynomial preserving recovery for high frequency wave propagation
• An unfitted finite element method, based on Nitsche's method, for elliptic interface problems.
• A boundary condition capturing method for Poisson's equation on irregular domains
• Solving elliptic problems with discontinuities on irregular domains -- the Voronoi interface method
• The polynomial-preserving recovery for higher order finite element methods in 2D and 3D
• Gradient recovery for elliptic interface problem. II: Immersed finite element methods
• A finite element method for the simulation of strong and weak discontinuities in solid mechanics
• High order matched interface and boundary method for elliptic equations with discontinuous coefficients and singular sources
• A cut finite element method for a Stokes interface problem
• The finite element method for elliptic equations with discontinuous coefficients
• 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)
• Numerical method for solving matrix coefficient elliptic equation with sharp-edged interfaces
• The extended finite element method for rigid particles in Stokes flow
• CutFEM: Discretizing geometry and partial differential equations
• The extended/generalized finite element method: An overview of the method and its applications
• The immersed boundary method
• Nitsche's method for interface problems in computa-tional mechanics
• The superconvergent patch recovery anda posteriori error estimates. Part 1: The recovery technique
• The superconvergent patch recovery anda posteriori error estimates. Part 2: Error estimates and adaptivity
• Elastic crack growth in finite elements with minimal remeshing
• The Immersed Interface Method for Elliptic Equations with Discontinuous Coefficients and Singular Sources
• A Fast Iterative Algorithm for Elliptic Interface Problems
• A finite element method on composite grids based on Nitsche's method
• Asymptotically Exact A Posteriori Error Estimators, Part II: General Unstructured Grids
• A Posteriori Error Estimates Based on the Polynomial Preserving Recovery
• An immersed finite element space and its approximation capability
• Analysis of recovery type a posteriori error estimators for mildly structured grids
• Partially Penalized Immersed Finite Element Methods For Elliptic Interface Problems
• Flux Recovery and Superconvergence of Quadratic Immersed Interface Finite Elements
• A New Finite Element Gradient Recovery Method: Superconvergence Property
• Accurate Solution and Gradient Computation for Elliptic Interface Problems with Variable Coefficients
• Fictitious domain methods using cut elements: III. A stabilized Nitsche method for Stokes’ problem
• The Mathematical Theory of Finite Element Methods
• The Immersed Interface Method

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