Back to Search
Start Over
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
- Source :
- Numerical Algorithms
- Publication Year :
- 2020
- Publisher :
- Springer Science and Business Media LLC, 2020.
-
Abstract
- In this paper, we study the numerical approximation of a general second order semilinear stochastic partial differential equation (SPDE) driven by a additive fractional Brownian motion (fBm) with Hurst parameter $H>\frac {1}{2}$ H > 1 2 and Poisson random measure. 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 $\mathcal {O}(h^{2}+\varDelta t)$ O ( h 2 + Δ t ) 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.
- Subjects :
- poisson random measure
Fractional Brownian motion
errors estimate
Discretization
Applied Mathematics
Numerical analysis
finite element method
fractional Brownian motion
Poisson random measure
010103 numerical & computational mathematics
Type (model theory)
Exponential integrator
VDP::Matematikk og Naturvitenskap: 400::Matematikk: 410
01 natural sciences
Measure (mathematics)
stochastic parabolic partial differential equations
010101 applied mathematics
Stochastic partial differential equation
Mathematics::Probability
timestepping methods
finite element methods
Applied mathematics
0101 mathematics
Mathematics
Subjects
Details
- ISSN :
- 15729265 and 10171398
- Volume :
- 88
- Database :
- OpenAIRE
- Journal :
- Numerical Algorithms
- Accession number :
- edsair.doi.dedup.....4c372eaa02f26151e7c5e791bbc35955