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This MATLAB code has been developed as part of my master's
thesis at the Norwegian University of Science and Technology during
the spring term of 2016.

	     Øystein Strengehagen Klemetsdal ([email protected])
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This repository contains an implementation of the virtual element
method for solving differential equations in two and three dimensions
using the open source MATLAB reservoir simulation toolbox (MRST, see
http://www.sintef.no/MRST). It is implemented for the propose of
testing the method, and comparing it to industry standard reservoir
simulation methods and grids.

VEM2D contains the following main functions:

---------------------------------------------------------------------------
- VEM2D_addBC: Adds boundary condition to existing or empty boundary
  condition struct.
	
- VEM2D_bc: Incorporates boundary conditions in global stiffness
  matrix and global load vector.

- VEM2D_glob: Assembles global stiffness matrix and load vector from
  local ones.

- VEM2D_loc: Computes local stiffness matrices and load vectors.

- VEM2D: Solves a given differential equation using the above
  functions.
---------------------------------------------------------------------------

In addition, it contains some auxiliary functions. See each
individual file for details and syntax.

Examples of usage of the software can be found in VEM2D/examples.m.

VEM3D contains the following main functions:

---------------------------------------------------------------------------
- VEM3D_addBC: Adds boundary condition to existing or empty boundary
  condition struct.
	
- VEM3D_bc: Incorporates boundary conditions in global stiffness
  matrix and global load vector.

- VEM3D_faceProjectors: Calculates the VEM projection operators for
  each face in the grid.

- VEM3D_glob: Assembles global stiffness matrix and load vector from
  local ones.

- VEM3D_loc: Computes local stiffness matrices and load vectors.

- VEM3D: Solves a given differential equation using the above
  functions.
---------------------------------------------------------------------------

In addition, it contains some auxiliary functions. See each
individual file for details and syntax.

Examples of usage of the software can be found in VEM3D/examples.m.

For further details, see:

Øystein Strengehagen Klemetsdal,
The virtual element method as a common framework for finite element
and finite difference methods - Numerical and theoretical analysis,
June 2016,
Masters thesis,
Department of Mathematics,
Norwegian University of Science and Technology.