fem2d_project_test

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

Licensing:

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

Related Data and Programs:

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.

Source Code:

• 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.