\(hp\)-finite element methods for singular perturbations
From MaRDI portal
Publication:1852960
DOI10.1007/b82946zbMath1021.65055OpenAlexW4239689675MaRDI QIDQ1852960
Publication date: 21 January 2003
Published in: Lecture Notes in Mathematics (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1007/b82946
singular perturbationerror estimatesboundary layersreaction-diffusion equationscorner layershp-finite element method
Nonlinear boundary value problems for linear elliptic equations (35J65) Singular perturbations in context of PDEs (35B25) Error bounds for boundary value problems involving PDEs (65N15) Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs (65N30) Research exposition (monographs, survey articles) pertaining to numerical analysis (65-02)
Related Items (70)
A \(C^{1}\)-conforming \(hp\) finite element method for fourth order singularly perturbed boundary value problems ⋮ Convergence analysis for finite element discretizations of the Helmholtz equation with Dirichlet-to-Neumann boundary conditions ⋮ Plane wave discontinuous Galerkin methods: exponential convergence of the \(hp\)-version ⋮ On Stability of Discretizations of the Helmholtz Equation ⋮ A first order system least squares method for the Helmholtz equation ⋮ An analysis of discretizations of the Helmholtz equation in \(L^2\) and in negative norms ⋮ On the stability of the boundary trace of the polynomial \(L^2\)-projection on triangles and tetrahedra ⋮ Mortar coupling of \(hp\)-discontinuous Galerkin and boundary element methods for the Helmholtz equation ⋮ Bernstein-Bézier Galerkin-characteristics finite element method for convection-diffusion problems ⋮ An exponential convergence approximation to singularly perturbed problems by log orthogonal functions ⋮ Superconvergence analysis of a finite element method for a two-parameter singularly perturbed problem ⋮ Adaptive Galerkin boundary element methods with panel clustering ⋮ Robust exponential convergence of \(hp\)-FEM in balanced norms for singularly perturbed reaction-diffusion problems: corner domains ⋮ Analytic regularity for a singularly perturbed system of reaction-diffusion equations with multiple scales ⋮ Wavenumber-explicit \textit{hp}-FEM analysis for Maxwell's equations with transparent boundary conditions ⋮ $hp$-Finite Elements for Fractional Diffusion ⋮ Efficient discretization and preconditioning of the singularly perturbed reaction-diffusion problem ⋮ A continuous \(hp\)-mesh model for adaptive discontinuous Galerkin schemes ⋮ A semi-Lagrangian Bernstein-Bézier finite element method for two-dimensional coupled Burgers' equations at high Reynolds numbers ⋮ Parameter-uniform numerical method for singularly perturbed convection-diffusion problem on a circular domain ⋮ On optimal \(L^2\)- and surface flux convergence in FEM ⋮ A Robust DPG Method for Singularly Perturbed Reaction-Diffusion Problems ⋮ Finite volume approximation of one-dimensional stiff convection-diffusion equations ⋮ Exponential Convergence of \(hp\)-FEM for the Integral Fractional Laplacian in Polygons ⋮ Exponential convergence of \textit{hp} FEM for spectral fractional diffusion in polygons ⋮ An $hp$ finite element method for a singularly perturbed reaction-convection-diffusion boundary value problem with two small parameters ⋮ A Bernstein-Bézier Lagrange-Galerkin method for three-dimensional advection-dominated problems ⋮ Optimal error estimates for Chebyshev approximations of functions with endpoint singularities in fractional spaces ⋮ Quantized tensor-structured finite elements for second-order elliptic PDEs in two dimensions ⋮ A class of discontinuous Petrov-Galerkin methods. III: Adaptivity ⋮ Exponential Convergence of a Generalized FEM for Heterogeneous Reaction-Diffusion Equations ⋮ An anisotropic \textit{hp}-mesh adaptation method for time-dependent problems based on interpolation error control ⋮ Computation of Quasi-Local Effective Diffusion Tensors and Connections to the Mathematical Theory of Homogenization ⋮ Wavenumber Explicit Analysis for Galerkin Discretizations of Lossy Helmholtz Problems ⋮ Robust numerical methods for singularly perturbed differential equations: a survey covering 2008-2012 ⋮ Nitsche-mortaring for singularly perturbed convection-diffusion problems ⋮ A posteriori error estimation for arbitrary order FEM applied to singularly perturbed one-dimensional reaction-diffusion problems. ⋮ Anisotropic \(hp\)-adaptive method based on interpolation error estimates in the \(L^q\)-norm ⋮ Boundary concentrated finite elements for optimal control problems with distributed observation ⋮ Modal spectral element method in curvilinear domains ⋮ A posteriori error estimations of a coupled mixed and standard Galerkin method for second order operators ⋮ An \(\mathcal{O}(p^3)\) \(hp\)-version FEM in two dimensions: preconditioning and post-processing ⋮ Use of tensor formats in elliptic eigenvalue problems ⋮ Tailored finite point method based on exponential bases for convection-diffusion-reaction equation ⋮ On superconvergence of Runge-Kutta convolution quadrature for the wave equation ⋮ Modular hp-FEM system HERMES and its application to Maxwell's equations ⋮ Arbitrary-level hanging nodes and automatic adaptivity in the \(hp\)-FEM ⋮ Uniform superconvergence analysis of the discontinuous Galerkin method for a singularly perturbed problem in 1-D ⋮ A spectral element method using the modal basis and its application in solving second‐order nonlinear partial differential equations ⋮ Pointwise approximation of corner singularities for a singularly perturbed reaction-diffusion equation in an $L$-shaped domain ⋮ A mixed hp FEM for the approximation of fourth‐order singularly perturbed problems on smooth domains ⋮ An adaptive strategy for \(hp\)-FEM based on testing for analyticity ⋮ Exponential Convergence of $hp$-Finite Element Discretization of Optimal Boundary Control Problems with Elliptic Partial Differential Equations ⋮ Low-rank tensor approximation of singularly perturbed boundary value problems in one dimension ⋮ A numerical study on Neumann-Neumann methods forhpapproximations on geometrically refined boundary layer meshes II. Three-dimensional problems ⋮ Shock capturing techniques for \(h p\)-adaptive finite elements ⋮ Predictor-corrector \(p\)- and \(h p\)-versions of the finite element method for Poisson's equation in polygonal domains ⋮ Tensor FEM for spectral fractional diffusion ⋮ L ∞ -Bounds for the L 2-Projection onto Linear Spline Spaces ⋮ Adjoint-based anisotropic \(hp\)-adaptation for discontinuous Galerkin methods using a continuous mesh model ⋮ A second-order overlapping Schwarz method for a 2D singularly perturbed semilinear reaction-diffusion problem ⋮ Nitsche type mortaring for singularly perturbed reaction-diffusion problems ⋮ Maximum norm error analysis of a 2d singularly perturbed semilinear reaction-diffusion problem ⋮ Preconditioning the Mass Matrix for High Order Finite Element Approximation on Tetrahedra ⋮ Virtual element method for singularly perturbed reaction-diffusion problems on polygonal domains ⋮ Optimal order uniform convergence in energy and balanced norms of weak Galerkin finite element method on Bakhvalov-type meshes for nonlinear singularly perturbed problems ⋮ High order approximations of the operator Lyapunov equation have low rank ⋮ Convergence analysis of an hp finite element method for singularly perturbed transmission problems in smooth domains ⋮ ℎ𝑝-version discontinuous Galerkin methods on essentially arbitrarily-shaped elements ⋮ Robust exponential convergence of \(hp\)-FEM in balanced norms for singularly perturbed reaction-diffusion equations
This page was built for publication: \(hp\)-finite element methods for singular perturbations
