.. _diffusion-poisson_functions: diffusion/poisson_functions.py ============================== **Description** Poisson equation with source term. Find :math:u such that: .. math:: \int_{\Omega} c \nabla v \cdot \nabla u = - \int_{\Omega_L} b v = - \int_{\Omega_L} f v p \;, \quad \forall v \;, where :math:b(x) = f(x) p(x), :math:p is a given FE field and :math:f is a given general function of space. This example demonstrates use of functions for defining material parameters, regions, parameter variables or boundary conditions. Notably, it demonstrates the following: 1. How to define a material parameter by an arbitrary function - see the function :func:get_pars() that evaluates :math:f(x) in quadrature points. 2. How to define a known function that belongs to a given FE space (field) - this function, :math:p(x), is defined in a FE sense by its nodal values only - see the function :func:get_load_variable(). In order to define the load :math:b(x) directly, the term dw_dot should be replaced by dw_integrate. .. image:: /../doc/images/gallery/diffusion-poisson_functions.png :download:source code  .. literalinclude:: /../sfepy/examples/diffusion/poisson_functions.py