A domain-specific embedded language in C++ for lowest-order discretizations of diffusive problems on general meshes

DOI10.1007/s10543-012-0403-3zbMath1262.65148OpenAlexW1992322819MaRDI QIDQ1944019

Jean-Marc Gratien, Christophe Prud'homme, Daniele A. Di Pietro

Publication date: 3 April 2013

Published in: BIT (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s10543-012-0403-3

zbMATH Keywords

numerical examplesfinite volume methodsfinite element methodsPetrov-Galerkin methodscell centered Galerkin methodsdomain specific embedded languagemimetic finite difference-type schemes

Mathematics Subject Classification ID

Boundary value problems for second-order elliptic equations (35J25) Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs (65N30) Finite difference methods for boundary value problems involving PDEs (65N06) Finite volume methods for boundary value problems involving PDEs (65N08)

Related Items

A hybrid high-order locking-free method for linear elasticity on general meshes ⋮ Implementation of discontinuous skeletal methods on arbitrary-dimensional, polytopal meshes using generic programming ⋮ An extension of the Crouzeix–Raviart space to general meshes with application to quasi-incompressible linear elasticity and Stokes flow

Uses Software

• Gmsh
• FreeFem++
• FEniCS
• SyFi
• Feel++

Cites Work

• Unnamed Item
• Unnamed Item
• On the flexibility of agglomeration based physical space discontinuous Galerkin discretizations
• A compact cell-centered Galerkin method with subgrid stabilization
• Mathematical aspects of discontinuous Galerkin methods.
• Automated solution of differential equations by the finite element method. The FEniCS book
• Cell centered Galerkin methods
• A mixed finite volume scheme for anisotropic diffusion problems on any grid
• Finite volume discretization with imposed flux continuity for the general tensor pressure equation
• Theory and practice of finite elements.
• Cell centered Galerkin methods for diffusive problems
• Lowest order methods for diffusive problems on general meshes: A unified approach to definition and implementation
• 3D Benchmark on Discretization Schemes for Anisotropic Diffusion Problems on General Grids
• Analysis of a discontinuous galerkin method for heterogeneous diffusion problems with low-regularity solutions
• Discretization of heterogeneous and anisotropic diffusion problems on general nonconforming meshes SUSHI: a scheme using stabilization and hybrid interfaces
• Feel++ : A computational framework for Galerkin Methods and Advanced Numerical Methods
• A compact multipoint flux approximation method with improved robustness
• The G method for heterogeneous anisotropic diffusion on general meshes
• Gmsh: A 3-D finite element mesh generator with built-in pre- and post-processing facilities
• An Interior Penalty Finite Element Method with Discontinuous Elements
• Discretization on Unstructured Grids for Inhomogeneous, Anisotropic Media. Part I: Derivation of the Methods
• Discontinuous Galerkin and the Crouzeix–Raviart element: Application to elasticity
• Unified Embedded Parallel Finite Element Computations via Software-Based Fréchet Differentiation
• A UNIFIED APPROACH TO MIMETIC FINITE DIFFERENCE, HYBRID FINITE VOLUME AND MIXED FINITE VOLUME METHODS
• Low Order Discontinuous Galerkin Methods for Second Order Elliptic Problems
• 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

This page was built for publication: A domain-specific embedded language in C++ for lowest-order discretizations of diffusive problems on general meshes