Analysis and optimization of inner products for mimetic finite difference methods on a triangular grid

DOI10.1016/j.matcom.2004.05.008zbMath1058.65115OpenAlexW2119352248MaRDI QIDQ1887822

Richard Liska, Mikhail J. Shashkov, Victor G. Ganzha

Publication date: 22 November 2004

Published in: Mathematics and Computers in Simulation (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.matcom.2004.05.008

zbMATH Keywords

condition numberLaplace equationsupport operator methoddiscrete gradient operatordiscrete divergence operatorTriangular gridMimetic finite difference method

Mathematics Subject Classification ID

Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation (35J05) Mesh generation, refinement, and adaptive methods for boundary value problems involving PDEs (65N50) Finite difference methods for boundary value problems involving PDEs (65N06)

Related Items

The mimetic finite difference method on polygonal meshes for diffusion-type problems, Flux reconstruction and solution post-processing in mimetic finite difference methods, A cell-centered diffusion scheme on two-dimensional unstructured meshes, Discrete normal vector field approximation via time scale calculus, Mimetic discretizations of elliptic control problems, A FAMILY OF MIMETIC FINITE DIFFERENCE METHODS ON POLYGONAL AND POLYHEDRAL MESHES, A residual based error estimator for the mimetic finite difference method, M-Adaptation in the mimetic finite difference method, Forward modelling of geophysical electromagnetic data on unstructured grids using an adaptive mimetic finite-difference method, Mimetic finite difference method

Uses Software

• QEPCAD
• REDUCE

Cites Work

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• Natural discretizations for the divergence, gradient, and curl on logically rectangular grids
• Partial cylindrical algebraic decomposition for quantifier elimination
• Adjoint operators for the natural discretizations of the divergence, gradient and curl on logically rectangular grids
• The effect of inner products for discrete vector fields on the accuracy of mimetic finite difference methods