Numerical Analysis: Numerical Methods for Partial Differential Equations

<p>The course is an optional course for second-cycle studies for a Master's degree in mathematics with a specialisation in numerical analysis, as well as for a master's degree in computational science. The purpose of the course is for the students to acquire in-depth knowledge of numerical methods for partial differential equations and get the opportunity to work with relevant computational problems and software in connection with partial differential equations.</p><p>The course gives an introduction to error estimates, convergence and stability, as well as existence and regularity of solutions to elliptic differential equations (PDEs). This is followed by an introduction to DUNE-FEM which discusses how elliptic PDEs can be discretized using the Finite Element Method (FEM).</p> <p>The course treats:</p> <ul> <li>Weak theory for elliptic PDEs: existence and error estimates</li> <li>Construction of Finite Elements, e.g. discretization grids, reference elements, degree-of-freedom (DOF) mappings</li> <li>Unified Form Language (UFL) for description of weak forms of partial differential equations</li> <li>Parallelization of Finite Element methods using domain decomposition</li> <li>Adaptive Finite Element</li> </ul>