Andrea Barth: Catalogue data in Spring Semester 2012 |
Name | Dr. Andrea Barth |
Department | Mathematics |
Relationship | Lecturer |
Number | Title | ECTS | Hours | Lecturers | |
---|---|---|---|---|---|
401-4606-00L | Numerical Analysis of Stochastic Partial Differential Equations | 8 credits | 4G | A. Barth, A. Lang | |
Abstract | Mathematical formulation of partial differential equations with random inputs, and numerical analysis of deterministic approximation methods for them: Karhunen-Loeve expansion of random fields, measures on Hilbert spaces, multilevel Finite Element methods, sparse tensor and polynomial chaos type approximation methods | ||||
Objective | The mathematical formulation of stochastic and random partial differential equations and the main discretization methods. | ||||
Content | 1 Preliminaries 1.1 Functional analysis 1.2 Probability theory 2 Stochastic partial diffrential equations 2.1 Gaussian measures 2.2 Wiener processes 2.3 Stochastic integration 2.4 Solutions of stochastic partial differential equations 2.5 Finite Element approximation 2.6 Noise approximation 2.7 (Multilevel) Monte Carlo methods 3 Random partial differential equations 3.1 Distributions on Banach spaces 3.2 Elliptic partial differential equation with stochastic right hand 3.2.1 Existence and uniqueness 3.2.2 Finite Element method 3.2.3 Full and sparse tensor approximations 3.3 Elliptic partial differential equation with stochastic operator 3.3.1 Existence and uniqueness 3.3.2 Finite Element method 3.3.3 (Multilevel) Monte Carlo methods 3.3.4 Stochastic Galerkin methods | ||||
Lecture notes | No lecture notes but handouts on selected topics will be provided. | ||||
Literature | 1. Stochastic Equations in Infinite Dimensions G. Da Prato and J. Zabczyk Cambridge Univ. Press (1992) 2. Taylor Approximations for Stochastic Partial Differential Equations A. Jentzen and P.E. Kloeden Siam (2011) 3. Numerical Solution of Stochastic Differential Equations P.E. Kloeden and E. Platen Springer Verlag (1992) 4. A Concise Course on Stochastic Partial Differential Equations C. Prévôt and M. Röckner Springer Verlag (2007) 5. Galerkin Finite Element Methods for Parabolic Problems V. Thomée Springer Verlag (2006) | ||||
Prerequisites / Notice | Functional analysis, numerical solution of elliptic and parabolic PDEs, probability theory, stochastic processes |