**fem2d_project_test**,
a MATLAB code which
calls fem2d_project(), which
projects a finite element method function.

The computer code and data files described and made available on this web page are distributed under the GNU LGPL license.

fem2d_project, a MATLAB code which projects a function f(x,y), given as data, into a given space associated with the finite element method (FEM) for piecewise linear triangular elements.

- fem2d_project_test.m, calls all the tests.
- fem2d_project_test.sh, runs all the tests.
- fem2d_project_test.txt, the output file.

**LINEAR** starts with sample data for the vector function f(x)=[ 1, 2x, 3y ],
on an 9 x 9 grid of equally spaced nodes from [0.0,8.0]x[0.0,8.0], and projects this onto
a piecewise linear finite element meshes defined on equally spaced grids of
dimension 4x4, 2x2 and 1x1.

- r8x8_t3_nodes.txt, the sample nodes, on an 8x8 grid.
- r8x8_t3_elements.txt, elements that can be used to form an 8x8 finite element mesh associated with the sample data. This is provide only so that a finite element function can be formed with the original sample data.
- r8x8_t3_values.txt, the sample nodal values.
- r4x4_t3_nodes.txt, the FEM nodes for a 4x4 grid.
- r4x4_t3_elements.txt, the FEM elements for a 4x4 grid.
- r4x4_t3_values.txt, the nodal values as projected from the 8x8 grid.
- r2x2_t3_nodes.txt, the FEM nodes for a 2x2 grid.
- r2x2_t3_elements.txt, the FEM elements for a 2x2 grid.
- r2x2_t3_values.txt, the nodal values as projected from the 8x8 grid.
- r1x1_t3_nodes.txt, the FEM nodes for a 1x1 grid.
- r1x1_t3_elements.txt, the FEM elements for a 1x1 grid.
- r1x1_t3_values.txt, the nodal values as projected from the 8x8 grid.

**CIRCLE** is a problem defined on a circular region with a small central hole.
The SAMPLE data uses 49,408 nodes and 98,304 elements. This data is to be projected
onto a finite element mesh (which is a simple coarsening of the mesh on which the
sample data was generated) that uses 12,416 nodes and 24,576 elements.

- circle_sample_nodes.txt, the sample nodes.
- circle_sample_elements.txt, the sample elements.
- circle_sample_values.txt, the sample values.
- circle_sample.png, a plot of the sample data.
- circle_fem_nodes.txt, the FEM nodes for a 4x4 grid.
- circle_fem_elements.txt, the FEM elements for a 4x4 grid.
- circle_fem_values.txt, the FEM nodal values as projected by FEM2D_PROJECT.
- circle_fem.png, a plot of the FEM data.
- circle.txt, the output file.