Finite volume methods
Publisher Summary This chapter focuses on finite volume methods. The finite volume
method is a discretization method that is well suited for the numerical simulation of various …
method is a discretization method that is well suited for the numerical simulation of various …
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 …
Basic principles of virtual element methods
We present, on the simplest possible case, what we consider as the very basic features of
the (brand new) virtual element method. As the readers will easily recognize, the virtual …
the (brand new) virtual element method. As the readers will easily recognize, the virtual …
The hitchhiker's guide to the virtual element method
The Hitchhiker's Guide to the Virtual Element Method | Mathematical Models and Methods in
Applied Sciences World Scientific Search This Journal Anywhere Quick Search in Journals …
Applied Sciences World Scientific Search This Journal Anywhere Quick Search in Journals …
[HTML][HTML] Equivalent projectors for virtual element methods
In the original virtual element space with degree of accuracy k, projector operators in the H 1-
seminorm onto polynomials of degree≤ k can be easily computed. On the other hand …
seminorm onto polynomials of degree≤ k can be easily computed. On the other hand …
Virtual elements for linear elasticity problems
We discuss the application of virtual elements to linear elasticity problems, for both the
compressible and the nearly incompressible case. Virtual elements are very close to mimetic …
compressible and the nearly incompressible case. Virtual elements are very close to mimetic …
Finite element exterior calculus: from Hodge theory to numerical stability
This article reports on the confluence of two streams of research, one emanating from the
fields of numerical analysis and scientific computation, the other from topology and …
fields of numerical analysis and scientific computation, the other from topology and …
The hybrid high-order method for polytopal meshes
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 …
Virtual element method for general second-order elliptic problems on polygonal meshes
We consider the discretization of a boundary value problem for a general linear second-
order elliptic operator with smooth coefficients using the Virtual Element approach. As in [AH …
order elliptic operator with smooth coefficients using the Virtual Element approach. As in [AH …
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 …