Bracket¶

This example employs adaptive multimesh hp-FEM to solve equations of linear elasticity.

Problem description¶

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.

Computational domain for the elastic bracket problem.

Sample results¶

The following figures show the two meshes and their polynomial degrees after several adaptive steps:

:math:`x` displacement -- mesh and polynomial degrees.

:math:`y` displacement -- mesh and polynomial degrees.

Note that the meshes are slightly different, not only in polynomial degrees, but also in element refinements.

Convergence comparison¶

Convergence graphs of adaptive h-FEM with linear elements, h-FEM with quadratic elements and hp-FEM are shown below.

DOF convergence graph for tutorial example 11-adapt-system.

The following graph shows convergence in terms of CPU time.

CPU convergence graph for example bracket

Comparison of the multimesh and single-mesh hp-FEM:

comparison of multimesh and single mesh hp-FEM

Bracket¶

Problem description¶

Sample results¶

Convergence comparison¶

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Convergence comparison¶

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