Log In Sign Up

A framework for implementing general virtual element spaces

by   Andreas Dedner, et al.

In this paper we develop a framework for the construction and implementation of general virtual element spaces based on projections built from constraint least squares problems. We introduce the concept of a VEM tuple which encodes all the necessary building blocks to formulate the projections. Using this generic approach we present a wide range of virtual element spaces with additional properties. We showcase this approach with examples and build H^k-conforming spaces for k=1,2 as well as divergence and curl free spaces. The framework has the advantage of being easily integrated into any existing finite element package and we demonstrate this within the DUNE framework.


page 19

page 20

page 22

page 23

page 24


Local L^2-bounded commuting projections in FEEC

We construct local projections into canonical finite element spaces that...

Immersed Virtual Element Methods for Maxwell Interface Problems in Three Dimensions

Finite element methods for Maxwell's equations are highly sensitive to t...

A class of finite dimensional spaces and H(div) conformal elements on general polytopes

We present a class of discretisation spaces and H(div)-conformal element...

Adaptive Development of Koncepts in Virtual Animats: Insights into the Development of Knowledge

As a part of our effort for studying the evolution and development of co...

General polytopial H(div) conformal finite elements and their discretisation spaces

We present a class of discretisation spaces and H(div)-conformal element...

Interpolation and stability properties of low order face and edge virtual element spaces

We analyse the interpolation properties of 2D and 3D low order virtual e...

On the maximum angle conditions for polyhedra with virtual element methods

Finite element methods are well-known to admit robust optimal convergenc...