Numerical Analysis: Numerical Methods for Partial Differential Equations

Education facts

Code: NUMN33

<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>

Entry requirements

Admission to the course requires English 6/b and at least 90 credits in natural sciences or engineering, of which at least 45 credits should be in mathematics and/or numerical analysis, including knowledge corresponding to the courses NUMA01 Computational Programming with Python, 7.5 credits, and NUMN32 Numerical Methods for Differential Equations, 7.5 credits.

Education offerings

Each offering has its own dates and conditions. Closed offerings are retained as history and do not mean that a new application is open.

• Numerical Analysis: Numerical Methods for Partial Differential Equations

  Lund University

  Lund

  Start date: 18 January 2027

  End date: 28 March 2027

  Pace of study: 50 %