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We introduce a new numerical method for solving time-harmonic acoustic scattering problems. The main focus is on plane waves scattered by smoothly varying material inhomogeneities. The proposed method works for any frequency $\omega$, but…
In this paper, we derive first-order Euler finite element discretization schemes for a time-dependent natural convection model with variable density (NCVD). The model is governed by the variable density Navier-Stokes equations coupled with…
During the last decades, international attempts have been made to develop realistic space weather prediction tools aiming to forecast the conditions on the Sun and in the interplanetary environment. These efforts have led to the development…
We present an accurate and efficient discretization approach for the adaptive discretization of typical model equations employed in numerical weather prediction. A semi-Lagrangian approach is combined with the TR-BDF2 semi-implicit time…
This article investigates adaptive mesh refinement procedures for the time-domain wave equation with Neumann boundary conditions, formulated as an equivalent hypersingular boundary integral equation. Space-adaptive and time-adaptive…
We consider a class of general SDEs with a jump integral term driven by a time-inhomogeneous Poisson random measure. We propose a two-parameters Euler-type scheme for this SDE class and prove an optimal rate for the strong convergence with…
An error analysis of trigonometric integrators (or exponential integrators) applied to spatial semi-discretizations of semilinear wave equations with periodic boundary conditions in one space dimension is given. In particular, optimal…
The full discretization of the semi-linear stochastic wave equation is considered. The discontinuous Galerkin finite element method is used in space and analyzed in a semigroup framework, and an explicit stochastic position Verlet scheme is…
We report on recent work on adaptive timestep control for weakly instationary gas flows [16, 18, 17] carried out within SFB 401, TPA3. The method which we implement and extend is a space-time splitting of adjoint error representations for…
A high-accuracy time discretization is discussed to numerically solve the nonlinear fractional diffusion equation forced by a space-time white noise. The main purpose of this paper is to improve the temporal convergence rate by modifying…
We prove a general criterion providing sufficient conditions under which a time-discretiziation of a given Stochastic Differential Equation (SDE) is a uniform in time approximation of the SDE. The criterion is also, to a certain extent,…
The space-time adaptive ADER-DG finite element method with LST-DG predictor and a posteriori sub-cell ADER-WENO finite-volume limiting was used for simulation of multidimensional reacting flows with detonation waves. The presented numerical…
Building on the well-posedness of the backward Kolmogorov partial differential equation in the Wasserstein space, we analyze the strong and weak convergence rates for approximating the unique solution of a class of McKean-Vlasov stochastic…
This paper investigates the approximation of stochastic delay differential equations (SDDEs) via the backward Euler-Maruyama (BEM) method under generalized monotonicity and Khasminskii-type conditions in the infinite horizon. First, by…
We present a stability and convergence analysis of the space-time continuous finite element method for the Hamiltonian formulation of the wave equation. More precisely, we prove a continuous dependence of the discrete solution on the data…
In this paper we present two strategies to enable "parallelization across the method" for spectral deferred corrections (SDC). Using standard low-order time-stepping methods in an iterative fashion, SDC can be seen as preconditioned Picard…
As a first step towards the numerical analysis of the stochastic primitive equations of the atmosphere and oceans, we study their time discretization by an implicit Euler scheme. From deterministic viewpoint the 3D Primitive Equations are…
We present an adaptive arbitrary-order accurate time-stepping numerical scheme for the flow of vesicles suspended in Stokesian fluids. Our scheme can be summarized as an approximate implicit spectral deferred correction (SDC) method.…
An Euler-type framework with equidistant step sizes is proposed for a class of time-changed stochastic differential equations.We establish the strong convergence rate of the standard Euler--Maruyama method under the global Lipschitz…
The increasing penetration of distributed energy resources (DERs) will decrease the rotational inertia of the power system and further degrade the system frequency stability. To address the above issues, this paper leverages the advanced…