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Such equations are more realistic in modelling real world phenomena. To the best of our knowledge, numerical schemes for such SPDE have been lacked in the scientific literature. The approximation is done with the standard finite element method in space and three Euler-type timestepping methods in time. More precisely the well-known linear implicit method, an exponential integrator and the exponential Rosenbrock scheme are used for time discretization. In contract to the current literature in the field, our linear operator is not necessary self-adjoint and we have achieved optimal strong convergence rates for SPDE driven by fBm and Poisson measure. The results examine how the convergence orders depend on the regularity of the noise and the initial data and reveal that the full discretization attains the optimal convergence rates of order<jats:inline-formula><jats:alternatives><jats:tex-math>$\\mathcal {O}(h^{2}+\\varDelta t)$<\/jats:tex-math><mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mml:mi>O<\/mml:mi><mml:mo>(<\/mml:mo><mml:msup><mml:mrow><mml:mi>h<\/mml:mi><\/mml:mrow><mml:mrow><mml:mn>2<\/mml:mn><\/mml:mrow><\/mml:msup><mml:mo>+<\/mml:mo><mml:mi>\u0394<\/mml:mi><mml:mi>t<\/mml:mi><mml:mo>)<\/mml:mo><\/mml:math><\/jats:alternatives><\/jats:inline-formula>for the exponential integrator and implicit schemes. Numerical experiments are provided to illustrate our theoretical results for the case of SPDE driven by the fBm noise.<\/jats:p>","DOI":"10.1007\/s11075-020-01041-1","type":"journal-article","created":{"date-parts":[[2020,12,7]],"date-time":"2020-12-07T05:02:52Z","timestamp":1607317372000},"page":"315-363","update-policy":"http:\/\/dx.doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":2,"title":["Optimal strong convergence rates of some Euler-type timestepping schemes for the finite element discretization SPDEs driven by additive fractional Brownian motion and Poisson random measure"],"prefix":"10.1007","volume":"88","author":[{"given":"Aurelien Junior","family":"Noupelah","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Antoine","family":"Tambue","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2020,12,7]]},"reference":[{"issue":"2","key":"1041_CR1","doi-asserted-by":"crossref","first-page":"79","DOI":"10.1515\/rose-2017-0008","volume":"25","author":"S Alberverio","year":"2017","unstructured":"Alberverio, S., Gawarecki, L., mandrekar, V., R\u00fcdiger, B., Sarkar, B.: Ito formula for mild solutions of SPDEs with Gaussian and non-Gaussian noise and applications to stability properties\u0302. 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