Polynomial preserving recovery for high frequency wave propagation

DOI10.1007/s10915-016-0312-8zbMath1398.65250OpenAlexW2537790887MaRDI QIDQ1704839

Hailong Guo, Xu Yang

Publication date: 13 March 2018

Published in: Journal of Scientific Computing (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s10915-016-0312-8

zbMATH Keywords

wave equationfinite element methodsuperconvergencegradient recoverypolynomial preservinghigh-frequency

Mathematics Subject Classification ID

Error bounds for boundary value problems involving PDEs (65N15) Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs (65N30) Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs (65M60) Mesh generation, refinement, and adaptive methods for boundary value problems involving PDEs (65N50)

Related Items (9)

Bloch theory-based gradient recovery method for computing topological edge modes in photonic graphene ⋮ A C⁰ linear finite element method for a second‐order elliptic equation in non‐divergence form with Cordes coefficients ⋮ Gradient recovery for elliptic interface problem. III: Nitsche's method ⋮ Convergence Analysis of a Discontinuous Galerkin Method for Wave Equations in Second-Order Form ⋮ A \(C^0\) linear finite element method for biharmonic problems ⋮ Gradient Recovery for Elliptic Interface Problem: I. Body-Fitted Mesh ⋮ A recovery-based linear \(C^0\) finite element method for a fourth-order singularly perturbed Monge-Ampère equation ⋮ Unnamed Item ⋮ Polynomial preserving recovery for a class of weak Galerkin finite element methods

Uses Software

• EasyMesh

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Optimal energy conserving local discontinuous Galerkin methods for second-order wave equation in heterogeneous media
• Frozen Gaussian approximation for high frequency wave propagation
• Energy conserving local discontinuous Galerkin methods for wave propagation problems
• Tailored finite point method for first order wave equation
• Gradient recovery for the Crouzeix-Raviart element
• Adaptive moving mesh methods
• Superconvergence analysis of the finite element method for nonlinear hyperbolic equations with nonlinear boundary condition
• Galerkin approximations for the two point boundary problem using continuous, piecewise polynomial spaces
• Anisotropic error estimates for elliptic problems
• Superconvergence results on mildly structured triangulations
• Superconvergence in Galerkin finite element methods
• Finite element solution of the Helmholtz equation with high wave number. I: The \(h\)-version of the FEM
• A fourth order accurate finite difference scheme for the elastic wave equation in second order formulation
• A superconvergent local discontinuous Galerkin method for the second-order wave equation on Cartesian grids
• The polynomial-preserving recovery for higher order finite element methods in 2D and 3D
• The highest order superconvergence for bi-$k$ degree rectangular elements at nodes: A proof of $2k$-conjecture
• Uniform-in-time superconvergence of the HDG methods for the acoustic wave equation
• Superconvergence of fully discrete splitting positive definite mixed FEM for hyperbolic equations
• Finite Element Solution of the Helmholtz Equation with High Wave Number Part II: The h-p Version of the FEM
• Can We Have Superconvergent Gradient Recovery Under Adaptive Meshes?
• Superconvergence of quadratic finite elements on mildly structured grids
• Enhancing eigenvalue approximation by gradient recovery on adaptive meshes
• A simple error estimator and adaptive procedure for practical engineerng analysis
• On the Superconvergence of Galerkin Approximations to Second-Order Hyperbolic Equations
• The superconvergent patch recovery anda posteriori error estimates. Part 1: The recovery technique
• Error Estimates for Finite Element Methods for Second Order Hyperbolic Equations
• Validation of a posteriori error estimators by numerical approach
• Asymptotically Exact A Posteriori Error Estimators, Part I: Grids with Superconvergence
• Each averaging technique yields reliable a posteriori error control in FEM on unstructured grids. Part I: Low order conforming, nonconforming, and mixed FEM
• A Posteriori Error Estimates Based on the Polynomial Preserving Recovery
• Analysis of recovery type a posteriori error estimators for mildly structured grids
• Enhancing Eigenvalue Approximation by Gradient Recovery
• A New Finite Element Gradient Recovery Method: Superconvergence Property
• The Mathematical Theory of Finite Element Methods
• Pre-asymptotic error analysis of CIP-FEM and FEM for the Helmholtz equation with high wave number. Part I: linear version
• $L^2 $-Estimates for Galerkin Methods for Second Order Hyperbolic Equations
• New anisotropic a priori estimates

This page was built for publication: Polynomial preserving recovery for high frequency wave propagation