fem2d_bvp_serene_test

fem2d_bvp_serene_test, an Octave code which calls fem2d_bvp_serene(), which applies the finite element method, (FEM) with serendipity elements, to a 2D boundary value problem over a rectangle.

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_bvp_serene, an Octave code which applies the finite element method (FEM), with serendipity elements, to a 2D boundary value problem (BVP) in a rectangle, and compares the computed and exact solutions with the L2 and seminorm errors.

Source Code:

• fem2d_bvp_serene_test.m, calls all the tests.
• fem2d_bvp_serene_test.sh, runs all the tests.
• fem2d_bvp_serene_test.txt, the output file.

• fem2d_bvp_serene_test01.m, a simple test in which the exact solution is a quadratic function.
• fem2d_bvp_serene_test02.m, makes some checks on the serendipity basis functions.
• fem2d_bvp_serene_test03.m, sets up a contrived problem so that the system matrix is formed using the Wathen matrix. It prints out one copy of the (scaled) element mass matrix, and compares it to a (scaled and permuted) copy of the Wathen matrix returned by Matlab's gallery('wathen',1,1) command.
• fem2d_bvp_serene_test04.m, repeats the calculation in fem2d_bvp_serene_test01(), but now uses the fem2d_bvp_serene_extend() function to extend the solution from the irregular serendipity grid to a matrix grid, which can then be plotted with the surf() command.
• fem2d_bvp_serene_test04.png, an image of the solution after extension.