Mihály Kovács (Pázmány Péter Catholic University, Hungary and Chalmers University/University of Gothenburg, Sweden)
Wednesday, June 16, 2021 - 15:00
Online Colloquium
Karl-Liebknecht-Str. 24/25, 14469 Potsdam
: A stationary fractional stochastic partial differential equation involves a fractional power of an integer order elliptic differential operator which makes the solution not directly accessible. In this talk we discuss numerical approximation of solutions to such fractional stochastic PDEs with additive spatial white noise on a bounded domain. The inverse operator is represented by a Bochner integral in the Dunford--Taylor functional calculus. By applying a quadrature formula to this integral representation, the inverse fractional power is approximated by a weighted sum of non-fractional resolvents evaluated at appropriate quadrature points. This yields standard integer order problems and the resolvents are then discretized in space by a continuous finite element method. This approach is combined with an approximation of the white noise based on the mass matrix of the finite element discretization. In this way an efficient numerical algorithm for computing samples of the approximate solution is obtained. The method is particularly interesting for real-world applications in spatial statistics, where fractional order stochastic partial differential equations with spatial white noise play an important role owing to their connection to Gaussian Matérn fields. This is a joint work with D. Bolin (Kaust) and K. Kirchner (Delft). If you wish to attend the talks, please contact Sylvie Paycha paycha@math.uni-potsdam.de for the login details.
submitted by Sylke Pfeiffer (sypfeiffer@math.uni-potsdam.de)