Error analysis of Petrov-Galerkin immersed finite element methods
DOI10.1016/j.cma.2022.115744OpenAlexW4310348092MaRDI QIDQ2678476
Xu Zhang, Cuiyu He, Shun Zhang
Publication date: 23 January 2023
Published in: Computer Methods in Applied Mechanics and Engineering (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1016/j.cma.2022.115744
a posteriori error estimatesa priori error estimatesimmersed finite elementPetrov-Galerkininterface problems
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)
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- Stable generalized finite element method (SGFEM)
- A weak formulation for solving elliptic interface problems without body fitted grid
- Interior penalty bilinear IFE discontinuous Galerkin methods for elliptic equations with discontinuous coefficient
- A numerical method for solving variable coefficient elliptic equation with interfaces
- A 3D immersed finite element method with non-homogeneous interface flux jump for applications in particle-in-cell simulations of plasma-lunar surface interactions
- Removing the cell resonance error in the multiscale finite element method via a Petrov-Galerkin formulation
- A priori error estimates for some discontinuous Galerkin immersed finite element methods
- Optimal convergence analysis of an immersed interface finite element method
- A comparison of the extended finite element method with the immersed interface method for elliptic equations with discontinuous coefficients and singular sources
- A \(p\)-th degree immersed finite element for boundary value problems with discontinuous coefficients
- The immersed interface method using a finite element formulation
- A multiscale finite element method for elliptic problems in composite materials and porous media
- New Cartesian grid methods for interface problems using the finite element formulation
- Superconvergence of immersed finite volume methods for one-dimensional interface problems
- A numerical method for solving three-dimensional elliptic interface problems with triple junction points
- An unfitted finite element method, based on Nitsche's method, for elliptic interface problems.
- A nonconforming immersed finite element method for elliptic interface problems
- Solving three-dimensional interface problems with immersed finite elements: a-priori error analysis
- An immersed finite element method for elliptic interface problems in three dimensions
- A Petrov-Galerkin finite element interface method for interface problems with Bloch-periodic boundary conditions and its application in phononic crystals
- Residual-based a posteriori error estimation for immersed finite element methods
- A cut finite element method for the Bernoulli free boundary value problem
- Shape optimization using the cut finite element method
- An immersed weak Galerkin method for elliptic interface problems
- An immersed discontinuous finite element method for the Stokes problem with a moving interface
- High degree discontinuous Petrov-Galerkin immersed finite element methods using fictitious elements for elliptic interface problems
- Superconvergence of immersed finite element methods for interface problems
- An immersed discontinuous finite element method for Stokes interface problems
- Numerical method for solving matrix coefficient elliptic equation with sharp-edged interfaces
- On the accuracy of finite element approximations to a class of interface problems
- CutFEM: Discretizing geometry and partial differential equations
- An Analysis of a Broken $P_1$-Nonconforming Finite Element Method for Interface Problems
- A new multiscale finite element method for high-contrast elliptic interface problems
- Generalized Finite Element Methods: Their Performance and Their Relation to Mixed Methods
- Three-dimensional immersed finite element methods for electric field simulation in composite materials
- Multiscale Finite Element Methods
- Convergence of a multiscale finite element method for elliptic problems with rapidly oscillating coefficients
- Edge Residuals Dominate A Posteriori Error Estimates for Low Order Finite Element Methods
- Local Bisection Refinement for N-Simplicial Grids Generated by Reflection
- An Unfitted Hybrid High-Order Method for Elliptic Interface Problems
- Inf‐sup stability of Petrov‐Galerkin immersed finite element methods for one‐dimensional elliptic interface problems
- An immersed finite element space and its approximation capability
- PIFE-PIC: Parallel Immersed Finite Element Particle-in-Cell for 3-D Kinetic Simulations of Plasma-Material Interactions
- A Bilinear Petrov-Galerkin Finite Element Method for Solving Elliptic Equation with Discontinuous Coefficients
- High-Order Multiscale Finite Element Method for Elliptic Problems
- Partially Penalized Immersed Finite Element Methods For Elliptic Interface Problems
- Solving Parabolic Moving Interface Problems with Dynamical Immersed Spaces on Unfitted Meshes: Fully Discrete Analysis
- An Unfitted Hybrid High-Order Method with Cell Agglomeration for Elliptic Interface Problems
- An extended finite element method for modeling crack growth with frictional contact.
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