Related papers: Implicit and semi-implicit second-order time stepp…
We establish sharp energy decay rates for a large class of nonlinearly first-order damped systems, and we design discretization schemes that inherit of the same energy decay rates, uniformly with respect to the space and/or time…
We analyze a semi-implicit finite volume scheme for the Gray--Scott system, a model for pattern formation in chemical and biological media. We prove unconditional well-posedness of the fully discrete problem and establish qualitative…
This paper aims to investigate a full numerical approximation of non-autonomous semilnear parabolic partial differential equations (PDEs) with nonsmooth initial data. Our main interest is on such PDEs where the nonlinear part is stronger…
We develop time integration methods in low-rank representation that can adaptively adjust approximation ranks to achieve a prescribed accuracy, while ensuring that these ranks remain proportional to the corresponding best approximation…
The article addresses the convergence of implicit and semi-implicit, fully discrete approximations of a class of nonlinear parabolic evolution problems. Such schemes are popular in the numerical solution of evolutions defined with the…
Discrete gradient methods are a powerful tool for the time discretization of dynamical systems, since they are structure-preserving regardless of the form of the total energy. In this work, we discuss the application of discrete gradient…
This work focuses on the development of a self adjusting multirate strategy based on an implicit time discretization for the numerical solution of hyperbolic equations, that could benefit from different time steps in different areas of the…
Semi-Lagrangian methods are numerical methods designed to find approximate solutions to particular time-dependent partial differential equations (PDEs) that describe the advection process. We propose semi-Lagrangian one-step methods for…
An efficient numerical scheme for solving transport equations for tokamak plasmas within an integrated modelling framework is presented. The plasma transport equations are formulated as diffusion-advection equations in two coordinates (a…
The main difficulty in studying numerical method for stochastic evolution equations (SEEs) lies in the treatment of the time discretization (J. Printems. [ESAIM Math. Model. Numer. Anal. (2001)]). Although fruitful results on numerical…
The time discretization of stochastic spectral fractional wave equation is studied by using the difference methods. Firstly, we exploit rectangle formula to get a low order time discretization, whose the strong convergence order is smaller…
We introduce a new family of high order accurate semi-implicit schemes for the solution of non-linear hyperbolic partial differential equations on unstructured polygonal meshes. The time discretization is based on a splitting between…
In this paper, numerical analysis is carried out for a class of history-dependent variational-hemivariational inequalities arising in contact problems. Three different numerical treatments for temporal discretization are proposed to…
This paper considers approximate smoothing for discretely observed non-linear stochastic differential equations. The problem is tackled by developing methods for linearising stochastic differential equations with respect to an arbitrary…
We present a novel and comparative analysis of finite element discretizations for a nonlinear Rosenau-Burgers model including a biharmonic term. We analyze both continuous and mixed finite element approaches, providing stability, existence,…
The aim of this paper is to obtain a posteriori error bounds of optimal order in time and space for the linear second-order wave equation discretized by the Newmark scheme in time and the finite element method in space. Error estimates are…
In many applications, the governing PDE to be solved numerically contains a stiff component. When this component is linear, an implicit time stepping method that is unencumbered by stability restrictions is often preferred. On the other…
Singular source terms in sub-diffusion equations may lead to the unboundedness of solutions, which will bring a severe reduction of convergence order of existing time-stepping schemes. In this work, we propose two efficient time-stepping…
The linearization of the meteorological equations around a specified reference state, usually applied in NWP to define the linear system of constant-coefficients semi-implicit schemes, is outlined as an unnecessarily restrictive approach…
Successive quadratic approximations, or second-order proximal methods, are useful for minimizing functions that are a sum of a smooth part and a convex, possibly nonsmooth part that promotes regularization. Most analyses of iteration…