Convergence analysis of the high-order mimetic finite difference method

DOI10.1007/s00211-009-0234-6zbMath1183.65132OpenAlexW2089338801MaRDI QIDQ841122

Konstantin N. Lipnikov, Lourenco Beirão da Veiga, Gianmarco Manzini

Publication date: 14 September 2009

Published in: Numerische Mathematik (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s00211-009-0234-6

zbMATH Keywords

convergencenumerical examplesa priori error estimatesmimetic finite difference methodsecond order elliptic problem

Mathematics Subject Classification ID

Boundary value problems for second-order elliptic equations (35J25) Error bounds for boundary value problems involving PDEs (65N15) Stability and convergence of numerical methods for boundary value problems involving PDEs (65N12) Finite difference methods for boundary value problems involving PDEs (65N06)

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Uses Software

• P2MESH

Cites Work

• Unnamed Item
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• Flux reconstruction and solution post-processing in mimetic finite difference methods
• Convergence analysis of the high-order mimetic finite difference method
• Higher-order mimetic methods for unstructured meshes
• A new finite volume scheme for anisotropic diffusion problems on general grids: convergence analysis
• A multilevel multiscale mimetic (M\(^3\)) method for two-phase flows in porous media
• High-order mimetic finite difference method for diffusion problems on polygonal meshes
• A new discretization methodology for diffusion problems on generalized polyhedral meshes
• The numerical solution of diffusion problems in strongly heterogeneous non-isotropic materials
• A finite volume method for the approximation of diffusion operators on distorted meshes
• A discrete operator calculus for finite difference approximations
• A local support-operators diffusion discretization scheme for quadrilateral \(r\)-\(z\) meshes
• The sensitivity and accuracy of fourth order finite-difference schemes on nonuniform grids in one dimension
• Constitutive equations for discrete electromagnetic problems over polyhedral grids
• A residual based error estimator for the mimetic finite difference method
• A mimetic discretization method for linear elasticity
• Ana posteriorierror estimator for the mimetic finite difference approximation of elliptic problems
• Mimetic finite differences for elliptic problems
• A Matrix Analysis Approach to Higher-Order Approximations for Divergence and Gradients Satisfying a Global Conservation Law
• New mixed finite element method on polygonal and polyhedral meshes
• Unified Analysis of Discontinuous Galerkin Methods for Elliptic Problems
• A Higher-Order Formulation of the Mimetic Finite Difference Method
• CONVERGENCE OF MIMETIC FINITE DIFFERENCE METHOD FOR DIFFUSION PROBLEMS ON POLYHEDRAL MESHES WITH CURVED FACES
• Algorithm 817: P2MESH
• Convergence of the Mimetic Finite Difference Method for Diffusion Problems on Polyhedral Meshes
• A FAMILY OF MIMETIC FINITE DIFFERENCE METHODS ON POLYGONAL AND POLYHEDRAL MESHES
• A tensor artificial viscosity using a mimetic finite differential algorithm