Syllabus
1. Introduction into the finite element method (weak solution, weak formulation, essential and natural boundary conditions, the Galerkin method, finite element, discrete solution)
2. Short introduction into the Python programming language (variables, operators, conditions, cycles, functions, units, I/O operations)
3. The basics of FEniCS software (computational mesh, spaces of basis function, boundary conditions, linear problem)
4. Time discretization
5. Nonlinear problems
6. Visualization in ParaView
7. Complex computational meshes (Gmsh)
8. Selected problems: Stokes flow of incompressible fluid, heat transfer equation, thermal convection, plasticity, viscoelastic deformation, free surface, thermo-chemical convection, ...
Annotation
Computer modeling is an essential tool for studying solar system bodies. The partial differential equations of continuum mechanics and thermodynamics that describe their internal evolution are solved by different methods
(finite element/difference/volume, spectral, etc.). The possibility to solve problems on complex and time evolving domains and straightforward implementation of boundary conditions are the main advantages of finite element method.