FINITE ElEMENT METHODS APPLIED TO GROUNDWATER MODEL PROBLEMS, IMPLEMENTED WITH THE USE OF FEniCs

Abstract

In this thesis an attempt is made to discuss the finite element meth-ods and FEniCs. Its main objective is to provide a general overview offinite element method specially, variational formulation of partial differen-tial equations, and to illustrate how to get started with FEniCs through aseries of simple examples. The serious of examples demonstrate how to de-fine a variational formulation of partial differential equations, how to dealpartial differential equations with different boundary conditions, how todeal with nonlinear partial differential equations, time dependent partialdifferential equations with in FEniCs. It also deals how to generate meshusing finite element mesh generator called Gmsh and how to use that tosolve problems in FEniCs. Finally, apply our gained knowledge to solvethe Gray-Scott model problem and to deal real physical model problemsfrom groundwater flow modeling.