7 citations · 17 across the 10 of their papers we have counts for
10 papers
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…
Linearly convergent nonoverlapping domain decomposition methods for quasilinear parabolic equations
Emil Engström, Eskil Hansen
We prove linear convergence for a new family of modified Dirichlet--Neumann methods applied to quasilinear parabolic equations, as well as the convergence of the Robin--Robin metho…
Time-dependent Steklov--Poincaré operators and space-time Robin--Robin decomposition for the heat equation
Emil Engström, Eskil Hansen
Domain decomposition methods are a set of widely used tools for parallelization of partial differential equation solvers. Convergence is well studied for elliptic equations, but in…
Convergence Analysis of the Nonoverlapping Robin-Robin Method for Nonlinear Elliptic Equations
Emil Engström, Eskil Hansen
We prove convergence for the nonoverlapping Robin-Robin method applied to nonlinear elliptic equations with a -structure, including degenerate diffusion equations governed by th…
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…
Convergence analysis of domain decomposition based time integrators for degenerate parabolic equations
Monika Eisenmann, Eskil Hansen
Domain decomposition based time integrators allow the usage of parallel and distributed hardware, making them well-suited for the temporal discretization of parabolic systems, in g…
A full space-time convergence order analysis of operator splittings for linear dissipative evolution equations
Eskil Hansen, Erik Henningsson
The Douglas--Rachford and Peaceman--Rachford splitting methods are common choices for temporal discretizations of evolution equations. In this paper we combine these methods with s…
A Convergence Analysis of the Peaceman--Rachford Scheme for Semilinear Evolution Equations
Eskil Hansen, Erik Henningsson
The Peaceman--Rachford scheme is a commonly used splitting method for discretizing semilinear evolution equations, where the vector fields are given by the sum of one linear and on…
Additive domain decomposition operator splittings -- convergence analyses in a dissipative framework
Eskil Hansen, Erik Henningsson
We analyze temporal approximation schemes based on overlapping domain decompositions. As such schemes enable computations on parallel and distributed hardware, they are commonly us…
High order splitting schemes with complex timesteps and their application in mathematical finance
Philipp Doersek, Eskil Hansen
High order splitting schemes with complex timesteps are applied to Kolmogorov backward equations stemming from stochastic differential equations in Stratonovich form. In the settin…