.. _diffusion-sinbc: diffusion/sinbc.py ================== **Description** Laplace equation with Dirichlet boundary conditions given by a sine function and constants. Find :math:t such that: .. math:: \int_{\Omega} c \nabla s \cdot \nabla t = 0 \;, \quad \forall s \;. The :class:sfepy.discrete.fem.meshio.UserMeshIO class is used to refine the original two-element mesh before the actual solution. The FE polynomial basis and the approximation order can be chosen on the command-line. By default, the fifth order Lagrange polynomial space is used, see define() arguments. This example demonstrates how to visualize higher order approximations of the continuous solution. The adaptive linearization is applied in order to save viewable results, see both the options keyword and the post_process() function that computes the solution gradient. The linearization parameters can also be specified on the command line. The Lagrange or Bernstein polynomial bases support higher order DOFs in the Dirichlet boundary conditions, unlike the hierarchical Lobatto basis implementation, compare the results of:: sfepy-run sfepy/examples/diffusion/sinbc.py -d basis=lagrange sfepy-run sfepy/examples/diffusion/sinbc.py -d basis=bernstein sfepy-run sfepy/examples/diffusion/sinbc.py -d basis=lobatto Use the following commands to view each of the results of the above commands (assuming default output directory and names):: sfepy-view 2_4_2_refined_t.vtk -2 -f t:wt sfepy-view 2_4_2_refined_grad.vtk -2 .. image:: /../doc/images/gallery/diffusion-sinbc_grad.png .. image:: /../doc/images/gallery/diffusion-sinbc_t.png :download:source code  .. literalinclude:: /../sfepy/examples/diffusion/sinbc.py