fem_basis_2013_fsu

fem_basis_2013_fsu, "The Finite Element Basis for Simplices in Arbitrary Dimension", an informal technical report which describes a procedure for defining and evaluating a finite element basis for simplices. The polynomial degree of the basis set and the spatial dimension of the simplex are both arbitrary. The report was written at Florida State University in 2013.

• fem_basis_2013_fsu.tex
• fem_basis_2013_fsu.pdf

Files you may copy include:

• area_basis.png, illustrates how triangular barycentric coordinates are ratios of subtriangle areas to the triangle area.
• convex_combination.png, illustrates how a line segment is generated by convex combinations of its endpoints.
• convex_combination_basis.png, a finite element basis function in 1D, formed from convex combination coefficients.
• square_node13.png, a 2D finite element basis function.
• triangle_reference2.png, the reference triangle, with the coordinate lines associated with a fifth order polynomial basis.
• triangle_reference3.png, shows a node in the reference triangle, and, in red, the five coordinate lines which will each supply a linear factor resulting in a fifth-degree polynomial which will be zero at every node except the indicated one.
• xi1_and_xi2.m, a MATLAB program for creating an illustration.
• xi1_and_xi2.png, the (unrestricted) 1D coefficient functions.
• xi1_and_xi2_restricted.m, a MATLAB program for creating an illustration.
• xi1_and_xi2_restricted.png, the restricted 1D coefficient functions.