Study the behavior of an elliptical problem is often very difficult due to the geometry of the domain and the boundary conditions, so it is necessary to use numerical methods to find a solution. The finiteelement method has proven to be efficient to treat problems of non-regular geometry and complicated parameters. This research has taken as reference the Poisson problem with mixed boundary conditions. It has proved the existence and uniqueness of a weak solution verifying the hypothesis Lax-Milgram theorem.The domain is discretized into triangular elements with three nodes and a degree of freedom per node and to discretize the differential equation has been used Galerkin method.

Study the behavior of an elliptical problem is often very difficult due to the geometry of the domain and the boundary conditions, so it is necessary to use numerical methods to find a solution. The finiteelement method has proven to be efficient to treat problems of non-regular geometry and complicated parameters. This research has taken as reference the Poisson problem with mixed boundary conditions. It has proved the existence and uniqueness of a weak solution verifying the hypothesis Lax-Milgram theorem.The domain is discretized into triangular elements with three nodes and a degree of freedom per node and to discretize the differential equation has been used Galerkin method.