89 citations · 914 across the 31 of their papers we have counts for
31 papers
Weighted Laplace Spaces for Spectral Measures and Rational Approximation
Stefan Jakobsson, Alice Kozakevicius, Stig Larsson
We introduce the weighted Laplace space , an RKHS of Laplace transforms on , and study spectral measures in its dual space . For conforming FEM discretizatio…
Finite Element Approximation of the Cahn-Hilliard-Cook equation
Ali Mesforush, Stig Larsson, Mihály Kovács
We study the nonlinear stochastic Cahn-Hilliard equation per- turbed by additive colored noise. We show almost sure existence and regularity of solutions. We introduce spatial appr…
Finite element approximation of the linearized Cahn-Hilliard-Cook equation
Ali Mesforush, Stig Larsson
The linearized Cahn-Hilliard-Cook equation is discretized in the spatial variables by a standard finite element method. Strong convergence estimates are proved under suitable assum…
Parametric elliptic reconstructions and a posteriori error estimates for parabolic partial differential equations with small randomness in a Robin boundary condition
Nakidi Shravani, Gujji Murali Mohan Reddy, Amiya Kumar Pani +1
We obtain reliable a posteriori residual-based error estimates for parabolic partial differential equations with small randomness in a Robin-type boundary condition. The uncertaint…
An energy-based deep splitting method for the nonlinear filtering problem
Kasper Bågmark, Adam Andersson, Stig Larsson
The purpose of this paper is to explore the use of deep learning for the solution of the nonlinear filtering problem. This is achieved by solving the Zakai equation by a deep split…
Error estimates of the backward Euler-Maruyama method for multi-valued stochastic differential equations
Monika Eisenmann, Mihály Kovács, Raphael Kruse +1
In this paper, we derive error estimates of the backward Euler-Maruyama method applied to multi-valued stochastic differential equations. An important example of such an equation i…
A greedy algorithm for optimal heating in powder-bed-based additive manufacturing
Robert Forslund, Anders Snis, Stig Larsson
Powder-bed-based additive manufacturing involves melting of a powder bed using a moving laser or electron beam as a heat source. In this paper, we formulate an optimization scheme…
Analytical solution for heat conduction due to a moving Gaussian heat flux with piecewise constant parameters
Robert Forslund, Anders Snis, Stig Larsson
We provide an analytical solution of the heat equation in the half-space subject to a moving Gaussian heat flux with piecewise constant parameters. The solution is of interest in p…
Mittag-Leffler Euler integrator for a stochastic fractional order equation with additive noise
Mihály Kovács, Stig Larsson, Fardin Saedpanah
Motivated by fractional derivative models in viscoelasticity, a class of semilinear stochastic Volterra integro-differential equations, and their deterministic counterparts, are co…
On a randomized backward Euler method for nonlinear evolution equations with time-irregular coefficients
Monika Eisenmann, Mihály Kovács, Raphael Kruse +1
In this paper we introduce a randomized version of the backward Euler method, that is applicable to stiff ordinary differential equations and nonlinear evolution equations with tim…
Strong convergence of a fully discrete finite element approximation of the stochastic Cahn-Hilliard equation
Daisuke Furihata, Mihály Kovács, Stig Larsson +1
We consider the stochastic Cahn-Hilliard equation driven by additive Gaussian noise in a convex domain with polygonal boundary in dimension . We discretize the equation usi…
Quasi-optimality of Petrov-Galerkin discretizations of parabolic problems with random coefficients
Stig Larsson, Christian Mollet, Matteo Molteni
We consider a linear parabolic problem with random elliptic operator in the usual Gelfand triple setting. We do not assume uniform bounds on the coercivity and boundedness constant…
Discrete Variational Derivative Methods for the EPDiff equation
Stig Larsson, Takayasu Matsuo, Klas Modin +1
The aim of this paper is the derivation of structure preserving schemes for the solution of the EPDiff equation, with particular emphasis on the two dimensional case. We develop th…
Numerical solution of parabolic problems based on a weak space-time formulation
Stig Larsson, Matteo Molteni
We investigate a weak space-time formulation of the heat equation and its use for the construction of a numerical scheme. The formulation is based on a known weak space-time formul…
On the discretisation in time of the stochastic Allen-Cahn equation
Mihály Kovács, Stig Larsson, Fredrik Lindgren
We consider the stochastic Allen--Cahn equation perturbed by smooth additive Gaussian noise in a spatial domain with smooth boundary in dimension , and study the semidiscre…
Covariance structure of parabolic stochastic partial differential equations with multiplicative Lévy noise
Kristin Kirchner, Annika Lang, Stig Larsson
The characterization of the covariance function of the solution process to a stochastic partial differential equation is considered in the parabolic case with multiplicative Lévy n…
Full discretisation of semi-linear stochastic wave equations driven by multiplicative noise
Rikard Anton, David Cohen, Stig Larsson +1
A fully discrete approximation of the semi-linear stochastic wave equation driven by multiplicative noise is presented. A standard linear finite element approximation is used in sp…
Compressive Space-Time Galerkin Discretizations of Parabolic Partial Differential Equations
Stig Larsson, Christoph Schwab
We study linear parabolic initial-value problems in a space-time variational formulation based on fractional calculus. This formulation uses "time derivatives of order one half" on…
Weak error analysis for semilinear stochastic Volterra equations with additive noise
Adam Andersson, Mihály Kovács, Stig Larsson
We prove a weak error estimate for the approximation in space and time of a semilinear stochastic Volterra integro-differential equation driven by additive space-time Gaussian nois…
An a posteriori error estimate for Symplectic Euler approximation of optimal control problems
Jesper Karlsson, Stig Larsson, Mattias Sandberg +2
This work focuses on numerical solutions of optimal control problems. A time discretization error representation is derived for the approximation of the associated value function.…
Discontinuous Galerkin method for an integro-differential equation modeling dynamic fractional order viscoelasticity
Stig Larsson, Milena Racheva, Fardin Saedpanah
An integro-differential equation, modeling dynamic fractional order viscoelasticity, with a Mittag-Leffler type convolution kernel is considered. A discontinuous Galerkin method, b…
A weak space-time formulation for the linear stochastic heat equation
Stig Larsson, Matteo Molteni
We apply the well-known Banach-Necas-Babuska inf-sup theory in a stochastic setting to introduce a weak space-time formulation of the linear stochastic heat equation with additive…
Duality in refined Sobolev-Malliavin spaces and weak approximations of SPDE
Adam Andersson, Raphael Kruse, Stig Larsson
We introduce a new family of refined Sobolev-Malliavin spaces that capture the integrability in time of the Malliavin derivative. We consider duality in these spaces and derive a B…
On the backward Euler approximation of the stochastic Allen-Cahn equation
Mihály Kovács, Stig Larsson, Fredrik Lindgren
We consider the stochastic Allen-Cahn equation perturbed by smooth additive Gaussian noise in a spatial domain with smooth boundary in dimension , and study the semidiscret…