README

C++ implementation of the VEM in 2D for elliptic (transport-diffusion) problems

COMPILE AND RUN
To compile the code a Makefile is provided, so simply do:
make
To run the code, simply run the main program as:
./main_project

REQUIREMENTS
The code makes usage of the C++11 standard and the Eigen library. In particular, in the Makefile one should modify the path_to_eigen (which is now set as /usr/local/include/eigen3)

INPUT
A mesh file has to be provided in the following format:
1. list of points representing the vertexes of the polygons as [pointX pointY]
2. list of indexes of the vertexes of i-th polygon (connectivity matrix), stored in a counterclockwise way
3. list of indexes denoting the vertexes which are on the domain boundary

In file main_project.cpp the following data have to be provided:
1. discretization degree k
2. name of the file containing the mesh
2. functions defining the diffusion coefficient, X- and Y- component of the transport term, source term, Dirichlet data, exact solution (to compute discretization error)

OUTPUT
Once run, the program will produce an output file called output.dat containing the list of points and the corresponding solution as [pointX pointY value]

EXAMPLE:
the file mesh_example.dat contains the mesh information for the discretization with a structured mesh of [0,1]x[0,1] made of N^2=16 squares.
the file output_example.dat contains the numerical results for a VEM discretization with k=1 and exact solution equal to u=x+y