Analysis of an interior penalty method for fourth order problems on polygonal domains

DOI10.1007/s10915-012-9612-9zbMath1261.65119OpenAlexW1975094578MaRDI QIDQ1936323

Thirupathi Gudi, Hari Shanker Gupta, Neela Nataraj

Publication date: 4 February 2013

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

Full work available at URL: https://doi.org/10.1007/s10915-012-9612-9

zbMATH Keywords

convergenceSobolev spaceserror estimatesfinite elementsnumerical experimentsunconditional stabilityDirichlet boundary conditionsdiscontinuous Galerkin methodinterior penalty methodfourth order elliptic problems

Mathematics Subject Classification ID

Boundary value problems for higher-order elliptic equations (35J40) Error bounds for boundary value problems involving PDEs (65N15) Stability and convergence of numerical methods for boundary value problems involving PDEs (65N12) Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs (65N30)

Related Items

A compact C⁰ discontinuous Galerkin method for Kirchhoff plates ⋮ An interior penalty method for distributed optimal control problems governed by the biharmonic operator ⋮ A Mixed Finite Element Scheme for Biharmonic Equation with Variable Coefficient and von Kármán Equations ⋮ A superconvergent \(C^0\) discontinuous Galerkin method for Kirchhoff plates: error estimates, hybridization and postprocessing ⋮ A C⁰ interior penalty method for the phase field crystal equation ⋮ An A Posteriori Analysis of $C^0$ Interior Penalty Methods for the Obstacle Problem of Clamped Kirchhoff Plates ⋮ Unconditional Energy Stability and Solvability for a C0 Interior Penalty Method for a Sixth-Order Equation Modeling Microemulsions ⋮ A $$\varvec{C}^0$$ C 0 Interior Penalty Method for Elliptic Distributed Optimal Control Problems in Three Dimensions with Pointwise State Constraints ⋮ A FrameWork for the Error Analysis of Discontinuous Finite Element Methods for Elliptic Optimal Control Problems and Applications toC⁰IP Methods ⋮ A C ⁰ interior penalty method for a fourth-order variational inequality of the second kind ⋮ A New Convergence Analysis of Finite Element Methods for Elliptic Distributed Optimal Control Problems with Pointwise State Constraints ⋮ Forty Years of the Crouzeix‐Raviart element

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• \(C^0\) interior penalty methods for fourth order elliptic boundary value problems on polygonal domains
• Mixed discontinuous Galerkin finite element method for the biharmonic equation
• A hybridizable and superconvergent discontinuous Galerkin method for biharmonic problems
• A new discontinuous Galerkin method for Kirchhoff plates
• \(hp\)-version a priori error analysis of interior penalty discontinuous Galerkin finite element approximations to the biharmonic equation
• A \(C^0\) discontinuous Galerkin formulation for Kirchhoff plates
• \(hp\)-version interior penalty DGFEMs for the biharmonic equation
• A posteriori error estimation and adaptive mesh-refinement techniques
• Continuous/discontinuous finite element approximations of fourth-order elliptic problems in structural and continuum mechanics with applications to thin beams and plates, and strain gradient elasticity
• A discontinuous Galerkin method for the plate equation
• Performance of a parallel mixed finite element implementation for fourth order clamped anisotropic plate bending problems in distributed memory environments
• Local discontinuous Galerkin methods for the Cahn-Hilliard type equations
• 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)
• Two-level additive Schwarz preconditioners for \(C^0\) interior penalty methods
• Geometrically nonlinear formulation for thin shells without rotation degrees of freedom
• A $\mathcal{C}^0$ Interior Penalty Method for a Fourth Order Elliptic Singular Perturbation Problem
• A new error analysis for discontinuous finite element methods for linear elliptic problems
• On existence of solution of the Dirichlet problem of fourth order partial differential equations with variable coefficients
• An a posteriori error estimator for a quadratic C0-interior penalty method for the biharmonic problem
• An improved finite-difference analysis of bending of thin rectangular elastic plates
• The Local Discontinuous Galerkin Method for Time-Dependent Convection-Diffusion Systems
• Isoparametric mixed finite element approximation of eigenvalues and eigenvectors of 4th order eigenvalue problems with variable coefficients
• Unified Analysis of Discontinuous Galerkin Methods for Elliptic Problems
• Discontinuous Galerkin methods for the biharmonic problem
• The Mathematical Theory of Finite Element Methods
• Multigrid Algorithms for C0 Interior Penalty Methods