Approximation of the biharmonic problem using P1 finite elements

DOI10.1515/JNUM.2011.001zbMath1261.65118OpenAlexW2032844095MaRDI QIDQ3006386

Mohamed Rhoudaf, Robert Eymard, Raphaèle Herbin

Publication date: 14 June 2011

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

Full work available at URL: https://doi.org/10.1515/jnum.2011.001

zbMATH Keywords

convergencenumerical resultserror estimatebiharmonic problemP1 finite element method

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 (6)

Unnamed Item ⋮ A staggered <scp>cell‐centered</scp> finite element method for Stokes problems with variable viscosity on general meshes ⋮ A recovery-based linear \(C^0\) finite element method for a fourth-order singularly perturbed Monge-Ampère equation ⋮ A new \(P_1\) weak Galerkin method for the biharmonic equation ⋮ Nonconforming P1 Finite Element for the Biharmonic Problem and Its Application to Stokes Problem ⋮ On MAC schemes on triangular delaunay meshes, their convergence and application to coupled flow problems

Cites Work

• \(C^0\) interior penalty methods for fourth order elliptic boundary value problems on polygonal domains
• Mixed discontinuous Galerkin finite element method for the biharmonic equation
• \(hp\)-version a priori error analysis of interior penalty discontinuous Galerkin finite element approximations to the biharmonic equation
• A fast finite difference method for biharmonic equations on irregular domains and its application to an incompressible Stokes flow
• \(hp\)-version interior penalty DGFEMs for the biharmonic equation
• A mixed finite volume element method based on rectangular mesh for biharmonic equations
• A Compact Difference Scheme for the Biharmonic Equation in Planar Irregular Domains
• A Fast Direct Solver for the Biharmonic Problem in a Rectangular Grid
• Discontinuous Galerkin methods for the biharmonic problem

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