The $h-p$ version of the finite element method with quasiuniform meshes

From MaRDI portal

Publication:3761628

Jump to:navigation, search

DOI10.1051/m2an/1987210201991zbMath0623.65113OpenAlexW2525823748MaRDI QIDQ3761628

Manil Suri, Ivo M. Babuška

Publication date: 1987

Published in: ESAIM: Mathematical Modelling and Numerical Analysis (Search for Journal in Brave)

Full work available at URL: https://eudml.org/doc/193500

zbMATH Keywords

numerical example corner singularity asymptotic L-shaped domain Error estimates h-p version of the finite element method quasiuniform meshes plain strain elasticity problem

Mathematics Subject Classification ID

Classical linear elasticity (74B05) Finite element methods applied to problems in solid mechanics (74S05) Error bounds for boundary value problems involving PDEs (65N15) 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

Analytic regularity of Stokes flow on polygonal domains in countably weighted Sobolev spaces, A posteriori error estimates for control problems governed by nonlinear elliptic equations in \(hp\)-FEM, A stable space-time FE method for the shallow water equations, The ultraspherical spectral element method, A new posteriori error estimates for a discontinuous Galerkin method for a reaction-diffusion problem, A unified a posteriori error estimate of local discontinuous Galerkin approximations for reactive transport problems, Polynomial extensions of compatible polynomial traces in three dimensions, Unlocking the secrets of locking: finite element analysis in planar linear elasticity, Residual-based a posteriori error estimates for the \(hp\) version of the finite element discretization of the elliptic Robin boundary control problem, Information-based numerical practice, The method of auxiliary mapping for the finite element solutions of elasticity problems containing singularities, Efficient simulation of cardiac electrical propagation using high-order finite elements. II: Adaptive \(p\)-version, A spectral collocation method for eigenvalue problems of compact integral operators, A stable Petrov-Galerkin method for convection-dominated problems, Adaptive \(hpq\)-finite element methods of hierarchical models for plate- and shell-like structures, Three-dimensional mixed explicit-implicit generalized Galerkin spectral element methods for high-speed turbulent compressible flows, \(hp\)-version discontinuous Galerkin methods for hyperbolic conservation laws, A priori error estimations of \(hp\)-finite element approximations for hierarchical models of plate- and shell-like structures, Error analysis of a coupled finite-infinite element method for an exterior Poisson problem, A priori error analyses of a stabilized discontinuous Galerkin method, Mixed finite element methods for nonlinear elliptic problems: The \(h-p\) version, A parallel \(hp\)-adaptive discontinuous Galerkin method for hyperbolic conservation laws, The treatment of nonhomogeneous Dirichlet boundary conditions by the p- version of the finite element method, An \textit{hp}-version error analysis of the discontinuous Galerkin method for linear elasticity, An adaptive refinement strategy for \(hp\)-finite element computations, The \(p\)-version of the boundary element method for weakly singular operators on piecewise plane open surfaces, \(hp\)-version a priori error analysis of interior penalty discontinuous Galerkin finite element approximations to the biharmonic equation, Construction of polynomial extensions in two dimensions and application to the \(h\)-\(p\) finite element method, Mixed discontinuous Galerkin finite element method for the biharmonic equation, Hodge decomposition methods for a quad-curl problem on planar domains, Convergence analysis of an energy based discontinuous Galerkin method for the wave equation in second-order form: \( h p\) version, Sparse polynomial approximation in positive order Sobolev spaces with bounded mixed derivatives and applications to elliptic problems with random loading, An \(hp\)-hybrid high-order method for variable diffusion on general meshes, Higher order weakly over-penalized symmetric interior penalty methods, A high-order discontinuous Galerkin method for nonlinear sound waves, A priori error analysis of a discontinuous Galerkin approximation for a kind of compressible miscible displacement problems, A coupled electro-thermal discontinuous Galerkin method, \(hp\) adaptive finite elements based on derivative recovery and superconvergence, Efficient simulation of cardiac electrical propagation using high order finite elements, \(L^2\)-error analysis of discontinuous Galerkin approximations for nonlinear Sobolev equations, A collection of 2D elliptic problems for testing adaptive grid refinement algorithms, 3D-based hierarchical models and \(hpq\)-approximations for adaptive finite element method of Laplace problems as exemplified by linear dielectricity, Non-conforming high order approximations of the elastodynamics equation, An hp finite element adaptive scheme to solve the Laplace model for fluid-solid vibrations, A lowest-order weak Galerkin method for linear elasticity, \(n\)-widths, sup-infs, and optimality ratios for the \(k\)-version of the isogeometric finite element method, A discontinuous \(hp\) finite element method for diffusion problems: 1-D analysis, A priori error estimates for interior penalty discontinuous Galerkin method applied to nonlinear Sobolev equations, Adaptive hpq finite element methods for the analysis of 3D-based models of complex structures. I: Hierarchical modeling and approximations, The weighted finite element method for elasticity equations on unbounded domains, A priori \(hp\)-estimates for discontinuous Galerkin approximations to linear hyperbolic integro-differential equations, Distributed Lagrange multiplier functions for fictitious domain method with spectral/hp element discretization, Error analysis of the spectral element method with Gauss-Lobatto-Legendre points for the acoustic wave equation in heterogeneous media, Analysis of Lavrentiev-finite element methods for data completion problems, A discontinuous Galerkin method for non-linear electro-thermo-mechanical problems: application to shape memory composite materials, Analysis and application of the IIPG method to quasilinear nonstationary convection-diffusion problems, Analysis of an interior penalty discontinuous Galerkin scheme for two phase flow in porous media with dynamic capillary effects, The problem of membrane locking in finite element analysis of cylindrical shells, Locking effects in the finite element approximation of elasticity problems, A discontinuous Galerkin finite element method for swelling model of polymer gels, \(L^2\)-error estimates of the extrapolated Crank-Nicolson discontinuous Galerkin approximations for nonlinear Sobolev equations, The \(p\)-version of the finite element method for the elliptic boundary value problems with interfaces, A posteriori error estimates for \(hp\) finite element solutions of convex optimal control problems, Local high-order regularization and applications to \(hp\)-methods, Adaptive energy minimisation for \(hp\)-finite element methods, Discontinuous Galerkin methods for coupled flow and reactive transport problems, A posteriori discontinuous Galerkin error estimator for linear elasticity, Mixed finite element methods for two-body contact problems, A note on the design of \(hp\)-adaptive finite element methods for elliptic partial differential equations, An unconditionally stable space-time FE method for the Korteweg-de Vries equation, Error estimates for the scaled boundary finite element method, Iterative Galerkin discretizations for strongly monotone problems, A coupling of mixed and discontinuous Galerkin finite element methods for poroelasticity, An extension theorem for polynomials on triangles, Analysis of \(hp\) discontinuous Galerkin methods for incompressible two-phase flow, Approximation results for spectral methods with domain decomposition, Stability analysis of polytopic discontinuous Galerkin approximations of the Stokes problem with applications to fluid-structure interaction problems, On \(L^2\)-error estimate for nonsymmetric interior penalty Galerkin approximation to linear elliptic problems with nonhomogeneous Dirichlet data, On \(hp\)-error estimation in the BEM for a three-dimensional Helmholtz exterior problem, Flowfield-dependent mixed explicit-implicit (FDMEI) methods for high and low speed and compressible and incompressible flows, Toward a universal h-p adaptive finite element strategy. I: Constrained approximation and data structure, Toward a universal h-p adaptive finite element strategy. II: A posteriori error estimation, Toward a universal h-p adaptive finite element strategy. III: Design of h-p meshes, The h-p version of the finite element method for problems with nonhomogeneous essential boundary condition, Staggered grid hybrid-dual spectral element method for second-order elliptic problems. Application to high-order time splitting methods for Navier-Stokes equations, An adaptive high-order unfitted finite element method for elliptic interface problems, \(hp\)-version interior penalty DGFEMs for the biharmonic equation, Stability and convergence of nonconforming \(hp\) finite-element methods, Adaptive virtual element methods with equilibrated fluxes, On polynomial robustness of flux reconstructions., Boundary-hybrid finite elements and a posteriori error estimation, A discontinuous \(hp\) finite element method for convection-diffusion problems, Nodal high-order methods on unstructured grids. I: Time-domain solution of Maxwell's equations, Theory and approximation of quasistatic frictional contact problems, Dynamically adapted mesh refinement for combustion front tracking., Finite element analysis of a holonomic elastic-plastic problem, Additive Schwarz algorithms for solving \(hp\)-version finite element systems on triangular meshes, The p- and h-p versions of the finite element method. An overview, A priori and a posteriori error analysis of \textit{hp} spectral element discretization for optimal control problems with elliptic equations, Residual-based \textit{a posteriori} error estimates for \textit{hp} finite element solutions of semilinear Neumann boundary optimal control problems, Unnamed Item, A Posteriori Error Estimates for $hp$ Spectral Element Approximation of Elliptic Control Problems with Integral Control and State Constraints, A priori error estimation of \(hp\)-finite element approximations of frictional contact problems with normal compliance, Polynomial extension operators. Part III, hp-adaptive extended finite element method, HP DISCONTINUOUS GALERKIN APPROXIMATIONS FOR THE STOKES PROBLEM, On a nonoverlapping additive <scp>S</scp>chwarz method for h‐p discontinuous <scp>G</scp>alerkin discretization of elliptic problems, The $hp$-local discontinuous Galerkin method for low-frequency time-harmonic Maxwell equations, Basic principles of hp virtual elements on quasiuniform meshes, The $h-p$ version of the boundary element method on polygonal domains with quasiuniform meshes, Unnamed Item, Error estimation and anisotropic mesh refinement for 3D laminar aerodynamic flow simulations, A finite element method using singular functions for Poisson equations: Mixed boundary conditions, Convergence analysis of a discontinuous finite element formulation based on second-order derivatives, A first-second order splitting method for a third-order partial differential equation, $C^0$ Interior Penalty Methods for an Elliptic Distributed Optimal Control Problem on Nonconvex Polygonal Domains with Pointwise State Constraints, Constructively well-posed approximation methods with unity inf–sup and continuity constants for partial differential equations, Anisotropic \(hp\)-mesh optimization technique based on the continuous mesh and error models, High order discontinuous Galerkin method for reduced flow models in fractured porous media, Relèvement polynômial de traces et applications, Exponential convergence of the \(hp\) virtual element method in presence of corner singularities, The $p$-version of the finite element method for elliptic equations of order $2l$, An MsFEM Approach Enriched Using Legendre Polynomials, Unnamed Item, $hp$-Version Space-Time Discontinuous Galerkin Methods for Parabolic Problems on Prismatic Meshes, Analysis of a full-discrete two-grid discontinuous Galerkin method for nonlinear parabolic equations, A two‐grid discontinuous Galerkin method for an incompressible miscible displacement problem, Construction and Analysis of HDG Methods for Linearized Shallow Water Equations, A Trefftz Polynomial Space-Time Discontinuous Galerkin Method for the Second Order Wave Equation, An arbitrarily high order unfitted finite element method for elliptic interface problems with automatic mesh generation, A combined mixed and discontinuous Galerkin method for compressible miscible displacement problem in porous media, An interior penalty discontinuous Galerkin method for a class of monotone quasilinear elliptic problems, Families of interior penalty hybridizable discontinuous Galerkin methods for second order elliptic problems, The \(p\)- and \(hp\)-versions of the virtual element method for elliptic eigenvalue problems, Numerical modeling of seismic waves by discontinuous spectral element methods, Thehp-version of the boundary element method with quasi-uniform meshes in three dimensions, Less is often more: applied inverse problems using \(hp\)-forward models, Spectral approximation of quadratic operator polynomials arising in photonic band structure calculations, A Discontinuous Galerkin Finite Element Method fOR Uniformly Elliptic Two Dimensional Oblique Boundary-Value Problems, Analysis of discontinuous Galerkin methods for multicomponent reactive transport problems, $H^2$-Stable Polynomial Liftings on Triangles, Enrichment of the nonconforming virtual element method with singular functions, A scalable exponential-DG approach for nonlinear conservation laws: with application to Burger and Euler equations, Superconvergence Analysis of Gradient Recovery Method for TM Model of Electromagnetic Scattering in the Cavity, Superconvergence Analysis of Gradient Recovery Method for TM Model of Electromagnetic Scattering in the Cavity, Discontinuous Galerkin Approximation of Flows in Fractured Porous Media on Polytopic Grids, Lagrange multiplier method with penalty for elliptic and parabolic interface problems, Error estimate of fully discrete discontinuous Galerkin approximation for the viscoelasticity type equation, Modular hp-FEM system HERMES and its application to Maxwell's equations, Analysis of a semidiscrete discontinuous Galerkin scheme for compressible miscible displacement problem, LOCAL CHEBYSHEV PROJECTION–INTERPOLATION OPERATOR AND APPLICATION TO THE h–p VERSION OF THE FINITE ELEMENT METHOD IN THREE DIMENSIONS, Locking Effects in the Finite Element Approximation of Plate Models, The \(p\) and \(hp\) finite element method for problems on thin domains, \(hp\)-discontinuous Galerkin methods for strongly nonlinear elliptic boundary value problems, The lifting of polynomial traces revisited, A direct coupling of local discontinuous Galerkin and boundary element methods, A systematic strategy for simultaneous adaptive \(hp\) finite element mesh modification using nonlinear programming, The optimal convergence of the \(h\)-\(p\) version of the boundary element method with quasiuniform meshes for elliptic problems on polygonal domains, The numerical methods for oscillating singularities in elliptic boundary value problems, The p‐version of the finite element method for domains with corners and for infinite domains, A posteriori error estimation and dynamic adaptivity for symmetric discontinuous Galerkin approximations of reactive transport problems, A dynamic adaptation scheme for general 3-D hybrid meshes, Uniform $hp$ convergence results for the mortar finite element method, Polynomial extension operators for $H^1$, $\boldsymbol {\mathit {H}}(\mathbf {curl})$ and $\boldsymbol {\mathit {H}}(\mathbf {div})$-spaces on a cube, Analysis for quadrilateral MITC elements for the Reissner-Mindlin plate problem, A finite element method dealing the singular points with a cut-off function, An $hp$-local discontinuous Galerkin method for some quasilinear elliptic boundary value problems of nonmonotone type, HP-finite element approximations on non-matching grids for partial differential equations with non-negative characteristic form, An explicit second order spectral element method for acoustic waves, Reprint of ``Construction of polynomial extensions in two dimensions and application to the \(h\)-\(p\) finite element method, On the Convergence Rate of the Cell Discretization Algorithm for Solving Elliptic Problems, New \textit{a posteriori} error estimates for \textit{hp} version of finite element methods of nonlinear parabolic optimal control problems, An \(hp\) finite element adaptive scheme to solve the Poisson problem on curved domains, A \(hk\) mortar spectral element method for the \(p\)-Laplacian equation, Galerkin Method with Discontinuous Basis Functions on Staggered Grips a Priory Estimates for the Homogeneous Dirichlet Problem, \(hp\) spectral element approximation for integral state constrained optimal control problems governed by harmonic equations, A posteriori error estimates of \(hp\) spectral element methods for optimal control problems with \(L^2\)-norm state constraint, Asymptotics of the generalized Gegenbauer functions of fractional degree, Априорные оценки локального разрывного метода Галеркина на разнесенных сетках для решения уравнения параболического типа в рамках однородной задачи Дирихле, On the coupling of local multilevel mesh refinement and ZZ methods for unilateral frictional contact problems in elastostatics, ℎ𝑝-Discontinuous Galerkin methods for the Helmholtz equation with large wave number, High-order polygonal discontinuous Petrov-Galerkin (PolyDPG) methods using ultraweak formulations, Predictor-corrector \(p\)- and \(h p\)-versions of the finite element method for Poisson's equation in polygonal domains, $hp$-Adaptation Driven by Polynomial-Degree-Robust A Posteriori Error Estimates for Elliptic Problems, A posteriori error estimates of \textit{hp} spectral element methods for integral state constrained elliptic optimal control problems, Hybrid Discontinuous Galerkin methods with relaxed H(div)-conformity for incompressible flows. Part II, Mass Conserving Mixed $hp$-FEM Approximations to Stokes Flow. Part II: Optimal Convergence, Residual-Based A Posteriori Error Estimates for $hp$-Discontinuous Galerkin Discretizations of the Biharmonic Problem, Convergence rate for a Radau hp collocation method applied to constrained optimal control, Superconvergent discontinuous Galerkin methods for nonlinear elliptic equations, hp-Version discontinuous Galerkin methods on polygonal and polyhedral meshes, Approximation of acoustic waves by explicit Newmark's schemes and spectral element methods, Optimal convergence rates ofhpmortar finite element methods for second-order elliptic problems, A priori error estimates of a combined mixed finite element and local discontinuous Galerkin method for an incompressible miscible displacement problem, Continuous interior penalty $hp$-finite element methods for advection and advection-diffusion equations, Unnamed Item, ℎ𝑝-version discontinuous Galerkin methods on essentially arbitrarily-shaped elements, Uniqueness of numerical solutions to nonlinear parabolic equations by a fully implicit discontinuous Galerkin method, Locking-Free Enriched Galerkin Method for Linear Elasticity, \(hp\)-optimal interior penalty discontinuous Galerkin methods for the biharmonic problem, Stable Lifting of Polynomial Traces on Triangles, A simple equilibration procedure leading to polynomial-degree-robust a posteriori error estimators for the curl-curl problem, Enhanced and efficient scaled boundary finite elements for mechanical problems under the action of body loads, Penalty-free any-order weak Galerkin FEMs for linear elasticity on quadrilateral meshes, An hp-mixed discontinuous Galerkin method for the biharmonic eigenvalue problem, An \textit{hp}-version interior penalty discontinuous Galerkin method for the quad-curl eigenvalue problem, An \(hp\) error analysis of a hybrid discontinuous mixed Galerkin method for linear viscoelasticity

Cites Work

Retrieved from "https://portal.mardi4nfdi.de/w/index.php?title=Publication:3761628&oldid=17301560"