6 papers · 1 filter
Error Bound and Stability Analysis for a Randomized Singly Diagonally Implicit Runge-Kutta Method
Monika Eisenmann, Marvin Jans, Raphael Kruse +1
A randomized Singly Diagonally Implicit Runge-Kutta (SDIRK) method, based on the randomized trapezoidal rule as the underlying quadrature scheme, is proposed. Every realization of…
Convergence analysis of Schwarz-like methods for degenerate elliptic-parabolic equations
Monika Eisenmann, Eskil Hansen
Convergence is proven for Schwarz-like methods applied to degenerate elliptic-parabolic equations with a -structure. This family of PDEs, e.g., arises when modelling nonlinear d…
Error bounds for full space-time splitting discretizations of semi-linear SPDEs -- with a focus on dG domain decompositions
Monika Eisenmann, Eskil Hansen, Marvin Jans
We consider a fully discretized numerical scheme for parabolic stochastic partial differential equations with multiplicative noise. Our abstract framework can be applied to formula…
A domain decomposition method for stochastic evolution equations
Evelyn Buckwar, Ana Djurdjevac, Monika Eisenmann
In recent years, SPDEs have become a well-studied field in mathematics. With their increase in popularity, it becomes important to efficiently approximate their solutions. Thus, ou…
A randomized operator splitting scheme inspired by stochastic optimization methods
Monika Eisenmann, Tony Stillfjord
In this paper, we combine the operator splitting methodology for abstract evolution equations with that of stochastic methods for large-scale optimization problems. The combination…
A variational approach to the sum splitting scheme
Monika Eisenmann, Eskil Hansen
Nonlinear parabolic equations are frequently encountered in applications and efficient approximating techniques for their solution are of great importance. In order to provide an e…