Computation of the Friedrichs and Poincare constants in 2D/3D

Computation of Friedrichs and Poincare constants in 2D/3D from generalized eigenvalue problems.

To run the code, type 'start_2D' or 'start_3D' in the MATLAB window.
Mass and stiffness matrices are assembled for nested uniform meshes (triangles in 2D and tetrahedral in 3D) starting from a coarse mesh (level=1 mesh) with few elements and ending up with a finest mesh (level=levels, where levels is predefined) with up to a milion of elements, depending on the available memory.

The Friedrichs', the Poincare are approximated from a generalized eigenvalue problems. Approximated values are compared with exact values if these are known (eg. for the rectangular domain in 2D and the cuboid domain in 3D) and corresponding eigenfunctions are visualized. Domains geometry can be easily changed by modifying input matrices: nodes2coords, elems2nodes, dirichlet. There is also an experimental computation of the Maxwell constant.
This code generalizes the original computations of the Friedrichs constant explained in the section 3.1. of [1]. The original code to [1] is saved in the 'original_code' folder and can be run as the file 'start_Friedrichs' in the MATLAB window. This code exploits vectorization concepts of FEM assemblies explained in [2] and [3] and runs therefore much faster.
Literature:
[1] Jan Valdman, Minimization of Functional Majorant in A Posteriori Error Analysis based on H(div) Multigrid-Preconditioned CG Method, Advances in Numerical Analysis, vol. 2009, Article ID 164519 (2009)

[2] Talal Rahman, Jan Valdman, Fast MATLAB assembly of FEM matrices in 2D and 3D: nodal elements. Applied Mathematics and Computation 219, 7151–7158 (2013)

[3] Immanuel Anjam, Jan Valdman, Fast MATLAB assembly of FEM matrices in 2D and 3D: Edge elements. Applied Mathematics and Computation 267, 252–263 (2015)

The paper can be downloaded from the author's web
http://sites.google.com/site/janvaldman/publications