Hierarchical hp FEM on rectangles in 2D

Implementation of rectangular hp-FEM with hierarchical shape functions that allows an effective assembly of mass and stiffness matrices.

This code provides eight examples that demonstrate implementation of hierarchical hp-FEM on rectangles in 2D from the paper:

Alexej Moskovka and Jan Valdman: MATLAB implementation of hp finite elements on rectangles, PPAM 2022, Lecture Notes in Computer Science (LNCS) 13827, pp. 287-299 (2023)

https://doi.org/10.1007/978-3-031-30445-3_24

Examples 1-4 provide visualization of 1D and 2D hiearchical shape functions together with the isoparametric transformation of a 2D shape function from a reference element on a quadrilateral.

Examples 5-6 assemble and display the indexing matrices for simple domain rectangulations.

Example 7 provides assembly times of mass and stiffness matrices for different h and p refinements.

Example 8 applies hp-FEM on solving a particular diffusion-reaction boundary value problem with uniform hp-refinements.