# Module for [Scientific Computing]

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## [Numerical Analysis of Partial Differential Equations] - [2015 Sommer]

Module | Code MH07 | Name Numerical Analysis of Partial Differential Equations | ||

| Credit Points 8 CP | Workload 240 | Duration 1 semester | Cycle 0 |

Methods | Lecture 4 h + Exercise course 2 h | |||

Objectives | MA Sc: To have a firm command of the most relevant methods for the numerical solution of initial-value and initital-value/boundary-value problems: Poisson, heat and wave equation/ MA Math: Ability to use typical analytical techniques from finite element | |||

Content | MA SC: * Theory of partial differential equations, type classification and properties of solutions * Finite difference method for elliptic boundary-value problems * Finite element method for elliptic boundary-value problems: discretization, a-priori and a-posteriori error analysis, grid adaptation * Solution methods for large linear systems: fixed-point iterations, Krylow methods and geometric multigrid methods * Methods for parabolic initial-value/boundary-value problems (heat equation) * Methods for hyperbolic problems (wave equation) MA Math: Introduction to elliptic partial differential equations; construction of the finite element method; a priori error estimates in energy and weaker norms; iterative solvers; multigrid and domain decomposi- tion methods; a posteriori error estimation; adaptive mesh refine- ment; mixed finite element methods for saddle point problems | |||

Learning outcomes | MA SC: * Analytic and algorithmic thinking * Application of methods from analysis and linear algebra * Independent solution of excercises with presentation MA Math: Foundations of finite element methods and their analysis | |||

Prerequisites | MA Math: Introduction to numerical analysis, Höhere Analysis (Lebesgue integration, Gauß theorem) | |||

Suggested previous knowledge | MA SC: Analysis I (MA1), Linear Algebra I (MA4), Introduction to Numerical Methods (MA7), Partial Differential Equations I (MC2) MA Math: Participation in the class "Implementation of numerical methods for partial differential equations" in this semester is recommended, but not required. | |||

Assessments | MA SC: weekly excercises with presentation, written or oral exam MA Math: Solution of homework exercises and a final oral exam. Details will be given by the lecturer at the beginning of the course. | |||

Literature | MA SC: Announced in the lecture MA Math: Grossmann, Roos(, Stynes): Numerical Treatment of Partial Differential Equations, English edition/ deutsche Ausgabe |