Poisson_problem_hd.py

In this script, we implement the hdMSEM for the Poisson problem with a manufactured solution in the crazy_mesh.

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Poisson_problem_hd.Poisson_hd(K, N, c, save=False)[source]
Parameters:

  • K (int) – We use a crazy mesh of K^3 elements. The domain decomposition is based on this crazy mesh.

  • N (int) – We use mimetic polynomials of degree N.

  • c (float) – The deformation factor of the crazy mesh is c,\ 0\leq c\leq 0.25.

  • save – Bool. If we save the coefficients of the variables.

Returns:

A tuple of several outputs:

  • The L^2\text{-error} of solution \boldsymbol{u}^h.

  • The H(\mathrm{div})\text{-error} of solution \boldsymbol{u}^h.

  • The L^2\text{-error} of solution \varphi^h.

  • The L^2\text{-error} of the projection, f^h.

  • The L^2\text{-error} of \nabla\cdot\boldsymbol{u}^h+f^h.

  • The L^\infty\text{-error} of \nabla\cdot\boldsymbol{u}^h+f^h.

  • The \widetilde{H}^1\text{-error} of solution \varphi^h.

Example:

>>> K = 2
>>> N = 3
>>> c = 0
>>> Poisson_hd(K, N, c) 
hdMSEM
L^2-error of u^h:  0.1535...

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