Finite volume schemes for diffusion equations: introduction to and review of modern methods
J Droniou - Mathematical Models and Methods in Applied …, 2014 - World Scientific
We present Finite Volume methods for diffusion equations on generic meshes, that received
important coverage in the last decade or so. After introducing the main ideas and …
important coverage in the last decade or so. After introducing the main ideas and …
Finite volume methods: foundation and analysis
T Barth, R Herbin, M Ohlberger - … of computational mechanics …, 2018 - Wiley Online Library
Finite volume methods are a class of discretization schemes resulting from the
decomposition of a problem domain into nonoverlap** control volumes. Degrees of …
decomposition of a problem domain into nonoverlap** control volumes. Degrees of …
The hybrid high-order method for polytopal meshes
DA Di Pietro, J Droniou - Number 19 in Modeling, Simulation and …, 2020 - Springer
Originally introduced in [146, 158], Hybrid High-Order (HHO) methods provide a framework
for the discretisation of models based on Partial Differential Equations (PDEs) with features …
for the discretisation of models based on Partial Differential Equations (PDEs) with features …
A weak Galerkin mixed finite element method for second order elliptic problems
J Wang, X Ye - Mathematics of Computation, 2014 - ams.org
A new weak Galerkin (WG) method is introduced and analyzed for the second order elliptic
equation formulated as a system of two first order linear equations. This method, called WG …
equation formulated as a system of two first order linear equations. This method, called WG …
Mimetic finite difference method
The mimetic finite difference (MFD) method mimics fundamental properties of mathematical
and physical systems including conservation laws, symmetry and positivity of solutions …
and physical systems including conservation laws, symmetry and positivity of solutions …
A hybrid high-order locking-free method for linear elasticity on general meshes
DA Di Pietro, A Ern - Computer Methods in Applied Mechanics and …, 2015 - Elsevier
We devise an arbitrary-order locking-free method for linear elasticity. The method relies on a
pure-displacement (primal) formulation and leads to a symmetric, positive definite system …
pure-displacement (primal) formulation and leads to a symmetric, positive definite system …
[BOOK][B] The mimetic finite difference method for elliptic problems
This book describes the theoretical and computational aspects of the mimetic finite
difference method for a wide class of multidimensional elliptic problems, which includes …
difference method for a wide class of multidimensional elliptic problems, which includes …
An arbitrary-order and compact-stencil discretization of diffusion on general meshes based on local reconstruction operators
DA Di Pietro, A Ern, S Lemaire - Computational Methods in Applied …, 2014 - degruyter.com
We develop an arbitrary-order primal method for diffusion problems on general polyhedral
meshes. The degrees of freedom are scalar-valued polynomials of the same order at mesh …
meshes. The degrees of freedom are scalar-valued polynomials of the same order at mesh …
Discretization of heterogeneous and anisotropic diffusion problems on general nonconforming meshes SUSHI: a scheme using stabilization and hybrid interfaces
A symmetric discretization scheme for heterogeneous anisotropic diffusion problems on
general meshes is developed and studied. The unknowns of this scheme are the values at …
general meshes is developed and studied. The unknowns of this scheme are the values at …
[BOOK][B] The gradient discretisation method
This monograph is dedicated to the presentation of The Gradient Discretisation Method
(GDM) and to some of its applications. It is intended for masters students, researchers and …
(GDM) and to some of its applications. It is intended for masters students, researchers and …