
Strong convergence of the backward Euler approximation for the finite element discretization of semilinear parabolic SPDEs with nonglobal Lipschitz drift driven by additive no
This paper deals with the backward Euler method applied to semilinear pa...
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Approximation of SPDE covariance operators by finite elements: A semigroup approach
The problem of approximating the covariance operator of the mild solutio...
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Strong approximation of Bessel processes
We consider the path approximation of Bessel processes and develop a new...
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Weak convergence of Galerkin approximations for fractional elliptic stochastic PDEs with spatial white noise
The numerical approximation of the solution u to a stochastic partial di...
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Optimal strong convergence rates of some Eulertype timestepping schemes for the finite element discretization SPDEs driven by additive fractional Brownian motion and Poisson r
In this paper, we study the numerical approximation of a general second ...
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Strong convergence rates on the whole probability space for spacetime discrete numerical approximation schemes for stochastic Burgers equations
The main result of this article establishes strong convergence rates on ...
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Tensor Rank bounds for Point Singularities in R^3
We analyze rates of approximation by quantized, tensorstructured repres...
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Weak convergence of fully discrete finite element approximations of semilinear hyperbolic SPDE with additive noise
We consider the numerical approximation of the mild solution to a semilinear stochastic wave equation driven by additive noise. For the spatial approximation we consider a standard finite element method and for the temporal approximation, a rational approximation of the exponential function. We first show strong convergence of this approximation in both positive and negative order norms. With the help of Malliavin calculus techniques this result is then used to deduce weak convergence rates for the class of twice continuously differentiable test functions with polynomially bounded derivatives. Under appropriate assumptions on the parameters of the equation, the weak rate is found to be essentially twice the strong rate. This extends earlier work by one of the authors to the semilinear setting. Numerical simulations illustrate the theoretical results.
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