A continuous/discontinuous Galerkin method and a priori error estimates for the biharmonic problem on surfaces

DOI10.1090/mcom/3179zbMath1368.65233arXiv1305.2740OpenAlexW1591693088MaRDI QIDQ5270828

Mats G. Larson, Karl Larsson

Publication date: 3 July 2017

Published in: Mathematics of Computation (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1305.2740

zbMATH Keywords

finite element methodnumerical examplesbiharmonic equationa priori error estimatesLaplace-Beltrami problemdiscrete energy normfourth-order elliptic PDEcontinuous/discontinuous Galerkin method

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) Boundary value problems on manifolds (58J32) Higher-order elliptic equations (35J30)

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Cites Work

• Tensor Decompositions and Applications
• \(C^0\) interior penalty methods for fourth order elliptic boundary value problems on polygonal domains
• Finite element approximation of the Laplace-Beltrami operator on a surface with boundary
• 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
• Einstein manifolds
• Analysis of the discontinuous Galerkin method for elliptic problems on surfaces
• An Adaptive Surface Finite Element Method Based on Volume Meshes
• The Finite Element Method: Theory, Implementation, and Applications
• A Finite Element Method for Elliptic Equations on Surfaces
• Finite elements on evolving surfaces
• Higher-Order Finite Element Methods and Pointwise Error Estimates for Elliptic Problems on Surfaces
• A stabilized finite element method for the Darcy problem on surfaces
• Positivity-Preserving Numerical Schemes for Lubrication-Type Equations
• Free Energy of a Nonuniform System. I. Interfacial Free Energy
• High Order Discontinuous Galerkin Methods for Elliptic Problems on Surfaces
• Finite element methods for surface PDEs
• The Mathematical Theory of Finite Element Methods
• An Adaptive Finite Element Method for the Laplace–Beltrami Operator on Implicitly Defined Surfaces
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