A new discretization methodology for diffusion problems on generalized polyhedral meshes
From MaRDI portal
Publication:1033384
DOI10.1016/j.cma.2006.10.028zbMath1173.76370OpenAlexW2107576752WikidataQ57386729 ScholiaQ57386729MaRDI QIDQ1033384
Franco Brezzi, Valeria Simoncini, Mikhail J. Shashkov, Konstantin N. Lipnikov
Publication date: 6 November 2009
Published in: Computer Methods in Applied Mechanics and Engineering (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1016/j.cma.2006.10.028
Diffusion (76R50) Finite difference methods applied to problems in fluid mechanics (76M20) Finite difference methods for initial value and initial-boundary value problems involving PDEs (65M06)
Related Items
\(H(\mathrm{div})\) and \(H(\mathbf{curl})\)-conforming virtual element methods ⋮ A finite volume method for approximating 3D diffusion operators on general meshes ⋮ Solution of the diffusion equation in multi‐material domains by sub‐division of elements along reconstructed interfaces ⋮ A virtual element generalization on polygonal meshes of the Scott-Vogelius finite element method for the 2-D Stokes problem ⋮ Low-order reconstruction operators on polyhedral meshes: application to compatible discrete operator schemes ⋮ Flux reconstruction and solution post-processing in mimetic finite difference methods ⋮ Convergence analysis of the high-order mimetic finite difference method ⋮ Equivalent projectors for virtual element methods ⋮ The nonconforming virtual element method for the Navier-Stokes equations ⋮ Topology optimization using polytopes ⋮ Fast computation of multiphase flow in porous media by implicit discontinuous Galerkin schemes with optimal ordering of elements ⋮ TRHD: Three-temperature radiation-hydrodynamics code with an implicit non-equilibrium radiation transport using a cell-centered monotonic finite volume scheme on unstructured-grids ⋮ Mimetic finite difference methods for Hamiltonian wave equations in 2D ⋮ A framework for developing a mimetic tensor artificial viscosity for Lagrangian hydrocodes on arbitrary polygonal meshes ⋮ Numerical method for coupled interfacial surfactant transport on dynamic surface meshes of general topology ⋮ A UNIFIED APPROACH TO MIMETIC FINITE DIFFERENCE, HYBRID FINITE VOLUME AND MIXED FINITE VOLUME METHODS ⋮ An enhanced octree polyhedral scaled boundary finite element method and its applications in structure analysis ⋮ Mimetic discretization of two-dimensional magnetic diffusion equations ⋮ Conforming virtual element approximations of the two-dimensional Stokes problem ⋮ On the virtual element method for three-dimensional linear elasticity problems on arbitrary polyhedral meshes ⋮ Numerical results for mimetic discretization of Reissner-Mindlin plate problems ⋮ A cell functional minimization scheme for parabolic problem ⋮ A displacement-based finite element formulation for general polyhedra using harmonic shape functions ⋮ A Hybrid High-Order Method for Quasilinear Elliptic Problems of Nonmonotone Type ⋮ The mimetic finite difference method for the 3D magnetostatic field problems on polyhedral meshes ⋮ Relationship between the vertex-centered linearity-preserving scheme and the lowest-order virtual element method for diffusion problems on star-shaped polygons ⋮ Discrete Helmholtz-Hodge decomposition on polyhedral meshes using compatible discrete operators ⋮ An improved monotone finite volume scheme for diffusion equation on polygonal meshes ⋮ Natural convection in porous annular domains: Mimetic scheme and family of steady states ⋮ The \textit{curved} mimetic finite difference method: allowing grids with curved faces ⋮ A mimetic discretization of the Reissner-Mindlin plate bending problem ⋮ A hybrid high-order method for a class of strongly nonlinear elliptic boundary value problems ⋮ An electrostatic particle-in-cell code on multi-block structured meshes ⋮ Convergence of the mimetic finite difference method for eigenvalue problems in mixed form ⋮ Virtual element methods for plate bending problems ⋮ A family of linearity-preserving schemes for anisotropic diffusion problems on arbitrary polyhedral grids ⋮ A cell functional minimization scheme for domain decomposition method on non-orthogonal and~non-matching meshes ⋮ A multilevel multiscale mimetic (M\(^3\)) method for two-phase flows in porous media ⋮ Effective shear viscosity and dynamics of suspensions of micro-swimmers from small to moderate concentrations ⋮ A mimetic discretization method for linear elasticity ⋮ Monotone finite volume schemes for diffusion equations on polygonal meshes ⋮ Monotone finite volume schemes for diffusion equations on unstructured triangular and shape-regular polygonal meshes ⋮ Spectral properties and conservation laws in mimetic finite difference methods for PDEs ⋮ High-order mimetic finite difference method for diffusion problems on polygonal meshes ⋮ A residual based error estimator for the mimetic finite difference method ⋮ BASIC PRINCIPLES OF VIRTUAL ELEMENT METHODS ⋮ Mimetic finite differences for nonlinear and control problems ⋮ The Hitchhiker's Guide to the Virtual Element Method ⋮ Finite volume schemes for diffusion equations: Introduction to and review of modern methods ⋮ M-Adaptation in the mimetic finite difference method ⋮ New perspectives on polygonal and polyhedral finite element methods ⋮ Analysis of stochastic mimetic finite difference methods and their applications in single-phase stochastic flows ⋮ Element agglomeration coarse Raviart–Thomas spaces with improved approximation properties ⋮ A two-level method for mimetic finite difference discretizations of elliptic problems ⋮ The finite volume scheme preserving extremum principle for diffusion equations on polygonal meshes ⋮ Innovative mimetic discretizations for electromagnetic problems ⋮ Ana posteriorierror estimator for the mimetic finite difference approximation of elliptic problems ⋮ Explicit geometric construction of \textit{sparse inverse mass matrices} for arbitrary tetrahedral grids ⋮ Multiscale VEM for the Biot consolidation analysis of complex and highly heterogeneous domains ⋮ Forward modelling of geophysical electromagnetic data on unstructured grids using an adaptive mimetic finite-difference method ⋮ A virtual element method for the coupled Stokes-Darcy problem with the Beaver-Joseph-Saffman interface condition ⋮ Mimetic finite difference method ⋮ Multiscale Methods for Subsurface Flow ⋮ Multiscale mixed/mimetic methods on corner-point grids ⋮ Unnamed Item ⋮ Mimetic finite difference method for the Stokes problem on polygonal meshes ⋮ Analysis of a mimetic finite difference approximation of flows in fractured porous media ⋮ Mimetic finite differences for elliptic problems ⋮ Bridging the hybrid high-order and hybridizable discontinuous Galerkin methods ⋮ Mixed virtual element methods for general second order elliptic problems on polygonal meshes ⋮ Mimetic finite difference approximation of flows in fractured porous media ⋮ Poincaré Type Inequalities for Vector Functions with Zero Mean Normal Traces on the Boundary and Applications to Interpolation Methods ⋮ Hybrid high-order methods for the elliptic obstacle problem ⋮ A nonconforming virtual element method for the Stokes problem on general meshes ⋮ A stress/displacement virtual element method for plane elasticity problems ⋮ The cell functional minimization scheme for the anisotropic diffusion problems on arbitrary polygonal grids ⋮ A mimetic discretization of elliptic obstacle problems ⋮ An extension of the Crouzeix–Raviart space to general meshes with application to quasi-incompressible linear elasticity and Stokes flow ⋮ A dual scaled boundary finite element formulation over arbitrary faceted star convex polyhedra ⋮ The high-order mixed mimetic finite difference method for time-dependent diffusion problems ⋮ Some virtual element methods for infinitesimal elasticity problems
Cites Work
- Unnamed Item
- Unnamed Item
- Algebraic multigrid (AMG): Experiences and comparisons
- The numerical solution of diffusion problems in strongly heterogeneous non-isotropic materials
- Approximation of boundary conditions for mimetic finite-difference methods
- Virtual bubbles and Galerkin-least-squares type methods (Ga.L.S.)
- Mixed and nonconforming finite element methods : implementation, postprocessing and error estimates
- Mixed and Hybrid Finite Element Methods
- Numerical Optimization
- Conservative Finite-Difference Methods on General Grids
- CONVERGENCE OF MIMETIC FINITE DIFFERENCE METHOD FOR DIFFUSION PROBLEMS ON POLYHEDRAL MESHES WITH CURVED FACES
- 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
This page was built for publication: A new discretization methodology for diffusion problems on generalized polyhedral meshes
