This repository provides several implementations of the Finite-Element-Method (FEM) for solving common problems in continuum mechanics. The underlying partial differential equations (PDEs) are solved utilizing the popular open-source platform FEniCS. All codes were written as part of my bachelor thesis "Numerical Modeling and Simulation of Convection in Earth's Outer Core via Finite Element Method". The thesis incorporates a thorough derivation of each problem and its (strong and weak) formulations.
The programs range from simple introductory problems such as the cavity flow to more advanced problems like the 2-dimensional mantle/core convection. The latter was realized by linking the Navier-Stokes-Equation with the Heat Equation using the Boussinesq-approximation (see thesis for detailed derivation). Furthermore, the derived PDEs were discretized with advanced numerical approaches, e.g. the implicit-explicit-scheme (IMEX, 2nd order), which is a multistep time-discretization scheme. Performances with respect to accuracy were analyzed on benchmark problems.
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The code was not intended for the public and was therefore not implemented according to specific coding standards.