English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Plus monthly

Global: Zendy Tools annual

Global: Zendy Tools monthly

Global: Zendy Free Plan

In this paper, we investigate a numerical approximation of a general secondorder semilinear parabolic non-autonomous stochastic partial differentialequation (SPDE) driven by additive noise. Numerical approximations forautonomous SPDEs are thoroughly investigated in the literature while thenon-autonomous case is not yet well understood.  We discretize the non-autonomous SPDE in space by the finite element methodand in time by the Magnus-type integrator. We provide a strong convergenceproof of the fully discrete scheme toward the mild solution in theroot-mean-square $L^2$ norm. Appropriate assumptions on the drift term and thenoise allow to achieve optimal convergence order in time greater than $1/2$,without any logarithmic reduction of convergence order in time. In particular,for trace class noise, we achieve optimal convergence orders$\mathcal{O}\left(h^{2-\epsilon}+\Delta t\right)$, where $\epsilon$ is apositive number small enough. Numerical simulations are provided to illustrateour theoretical results.

Magnus-type integrator for the finite element discretization of semilinear parabolic non-autonomous SPDEs driven by additive noise