Related papers: Continuous time integration for changing type syst…
We derive optimal $L^2$-error estimates for semilinear time-fractional subdiffusion problems involving Caputo derivatives in time of order $\alpha\in (0,1)$, for cases with smooth and nonsmooth initial data. A general framework is…
In this paper we study the numerical method for approximating the random periodic solution of semiliear stochastic evolution equations. The main challenge lies in proving a convergence over an infinite time horizon while simulating…
We consider a space-time variational formulation of the second-order wave equation, where integration by parts is also applied with respect to the time variable. Conforming tensor-product finite element discretisations with piecewise…
In this paper, we develop and analyze an integral fixed-time sliding mode control method for a scenario in which the system model is only partially known, utilizing Gaussian processes. We present two theorems on fixed-time convergence. The…
We propose efficient and parallel algorithms for the implementation of the high-order continuous time Galerkin method for dissipative and wave propagation problems. By using Legendre polynomials as shape functions, we obtain a special…
We introduce a family of proximal discontinuous Galerkin methods for variational inequalities, focusing on the obstacle problem as a didactic example. Each member of this family is born from applying a different well-known nonconforming…
We investigate a two-state conformational conversion system and introduce a novel structure-preserving numerical scheme that couples a local discontinuous Galerkin space discretization with the backward Euler time-integration method. The…
We formulate a stabilized quasi-optimal Petrov-Galerkin method for singularly perturbed convection-diffusion problems based on the variational multiscale method. The stabilization is of Petrov-Galerkin type with a standard finite element…
We introduce a classical computational method for quantum dynamics that relies on a global-in-time variational principle. Unlike conventional time-stepping approaches, our scheme computes the entire state trajectory over a finite time…
In the context of Galerkin discretizations of a partial differential equation (PDE), the modes of the classical method of Proper Orthogonal Decomposition (POD) can be interpreted as the ansatz and trial functions of a low-dimensional…
The discontinuous Petrov-Galerkin method is a minimal residual method with broken test spaces and is introduced for a nonlinear model problem in this paper. Its lowest-order version applies to a nonlinear uniformly convex model example and…
We obtain error bounds for a modified Chorin-Teman (Euler non-incremental) method for non inf-sup stable mixed finite elements applied to the evolutionary Navier-Stokes equations. The analysis of the classical Euler non-incremental method…
Solving optimal control problems to determine a stabilizing controller involves a significant computational effort. Time-varying optimal control provides a remedy by designing a tracking system, given as an ordinary differential equation,…
The Rosenbrock-Krylov family of time integration schemes is an extension of Rosenbrock-W methods that employs a specific Krylov based approximation of the linear system solutions arising within each stage of the integrator. This work…
This paper analyzes a space-time finite element method for fractional wave problems. The method uses a Petrov-Galerkin type time-stepping scheme to discretize the time fractional derivative of order $ \gamma $ ($1<\gamma<2$). We establish…
First order optimization algorithms play a major role in large scale machine learning. A new class of methods, called adaptive algorithms, were recently introduced to adjust iteratively the learning rate for each coordinate. Despite great…
For a general class of nonlinear port-Hamiltonian systems we develop a high-order time discretization scheme with certain structure preservation properties. The finite or infinite-dimensional system under consideration possesses a…
We study a fourth-order div problem and its approximation by the discontinuous Petrov-Galerkin method with optimal test functions. We present two variants, based on first and second-order systems. In both cases we prove well-posedness of…
Time-stepping $hp$-versions discontinuous Galerkin (DG) methods for the numerical solution of fractional subdiffusion problems of order $-\alpha$ with $-1<\alpha<0$ will be proposed and analyzed. Generic $hp$-version error estimates are…
In this paper, we develop the Galerkin-like method to address first-order integro-differential inclusions. Under compactness or monotonicity conditions, we obtain new results for the existence of solutions for this class of problems, which…