Git reference: Example bracket.
This example employs adaptive multimesh hp-FEM to solve equations of linear elasticity.
Our domain is a bracket loaded on its top edge and fixed to the wall:
\begin{eqnarray*} \bfu \!&=&\! 0 \ \ \ \ \ \rm{on}\ \Gamma_1 \\ \dd{u_2}{n} \!&=&\! f \ \ \ \ \ \rm{on}\ \Gamma_2 \\ \dd{u_1}{n} = \dd{u_2}{n} \!&=&\! 0 \ \ \ \ \ \rm{elsewhere.} \end{eqnarray*}
The dimensions are L = 0.7 m, T = 0.1 m and the force f = 10^3 N.
The following figures show the two meshes and their polynomial degrees after several adaptive steps:
Note that the meshes are slightly different, not only in polynomial degrees, but also in element refinements.
Convergence graphs of adaptive h-FEM with linear elements, h-FEM with quadratic elements and hp-FEM are shown below.
The following graph shows convergence in terms of CPU time.
Comparison of the multimesh and single-mesh hp-FEM: