De Rham Complexes for Weak Galerkin Finite Element Spaces

by   Chunmei Wang, et al.

Two de Rham complex sequences of the finite element spaces are introduced for weak finite element functions and weak derivatives developed in the weak Galerkin (WG) finite element methods on general polyhedral elements. One of the sequences uses polynomials of equal order for all the finite element spaces involved in the sequence and the other one uses polynomials of naturally decending orders. It is shown that the diagrams in both de Rham complexes commute for general polyhedral elements. The exactness of one of the complexes is established for the lowest order element.


page 1

page 2

page 3

page 4


Curved Elements in Weak Galerkin Finite Element Methods

A mathematical analysis is established for the weak Galerkin finite elem...

Numerical investigation on weak Galerkin finite elements

The weak Galerkin (WG) finite element method is an effective and flexibl...

Fast Evaluation of Finite Element Weak Forms Using Python Tensor Contraction Packages

In finite element calculations, the integral forms are usually evaluated...

Technical Report: Virtual X-ray imaging for higher-order finite element results

This work describes and demonstrates the operation of a virtual X-ray al...

The lowest-order stabilizer free Weak Galerkin Finite Element Method

Recently, a new stabilizer free weak Galerkin method (SFWG) is proposed,...

Sobolev Regularity of Isogeometric Finite Element Spaces with Degenerate Geometry Map

We investigate Sobolev regularity of bivariate functions obtained in Iso...

Towards an Extrinsic, CG-XFEM Approach Based on Hierarchical Enrichments for Modeling Progressive Fracture

We propose an extrinsic, continuous-Galerkin (CG), extended finite eleme...

Please sign up or login with your details

Forgot password? Click here to reset