Andrea Barth: Catalogue data in Spring Semester 2012

Name Dr. Andrea Barth
DepartmentMathematics
RelationshipLecturer

NumberTitleECTSHoursLecturers
401-4606-00LNumerical Analysis of Stochastic Partial Differential Equations8 credits4GA. Barth, A. Lang
AbstractMathematical 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
ObjectiveThe mathematical formulation of stochastic and random partial
differential equations and the main discretization methods.
Content1 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 notesNo lecture notes but handouts on selected topics will be provided.
Literature1. 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 / NoticeFunctional analysis, numerical solution of elliptic and parabolic PDEs, probability theory, stochastic processes