Related papers: Efficient second-order semi-implicit finite elemen…
The convergence analysis of a third-order scheme for the highly nonlinear Landau-Lifshitz-Gilbert equation with a non-convex constraint is considered. In this paper, we first present a fully discrete semi-implicit method for solving the…
This paper aims to develop and analyze a numerical scheme for solving the backward problem of semilinear subdiffusion equations. We establish the existence, uniqueness, and conditional stability of the solution to the inverse problem by…
In this work, an efficient approximation scheme has been proposed for getting accurate approximate solution of nonlinear partial differential equations with constant or variable coefficients satisfying initial conditions in a series of…
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…
A singularly perturbed linear system of second order partial differential equations of parabolic reaction-diffusion type with given initial and boundary conditions is considered. The leading term of each equation is multiplied by a small…
We consider the study of a numerical scheme for an initial- and Dirichlet boundary- value problem for a nonlinear Schr\"odinger equation. We approximate the solution using a, local (non-uniform) two level scheme in time (see C. Besse [6]…
We propose a second order, fully semi-Lagrangian method for the numerical solution of systems of advection-diffusion-reaction equations, which employs a semi-Lagrangian approach to approximate in time both the advective and the diffusive…
We propose a discrete functional analysis result suitable for proving compactness in the framework of fully discrete approximations of strongly degenerate parabolic problems. It is based on the original exploitation of a result related to…
We consider an elliptic partial differential equation in non-divergence form with a random diffusion matrix and random forcing term. To address this, we propose a mixed-type continuous finite element discretization in the physical domain,…
We introduce a discrete scheme for second order fully nonlinear parabolic PDEs with Caputo's time fractional derivatives. We prove the convergence of the scheme in the framework of the theory of viscosity solutions. The discrete scheme can…
We propose a new class of semi-implicit methods for solving nonlinear fractional differential equations and study their stability. Several versions of our new schemes are proved to be unconditionally stable by choosing suitable parameters.…
In this work, we develop and analyze a higher-order finite element method for the multidimensional fragmentation equation. To the best of our knowledge, this is the first study to establish a rigorous, conforming finite element framework…
In this paper, we develop a nonlinear reduction framework based on our recently introduced extended group finite element method. By interpolating nonlinearities onto approximation spaces defined with the help of finite elements, the…
We propose a high-order finite element method for linear fourth-order elliptic problems that is both nodally bound-preserving and mass-conservative, based on a variational inequality formulation. The method admits an equivalent strictly…
Motivated by the problem of solving the Einstein equations, we discuss high order finite difference discretizations of first order in time, second order in space hyperbolic systems.Particular attention is paid to the case when first order…
Several relaxation approximations to partial differential equations have been recently proposed. Examples include conservation laws, Hamilton-Jacobi equations, convection-diffusion problems, gas dynamics problems. The present paper focuses…
We consider the efficient numerical approximation of acoustic wave propagation in time domain by a finite element method with mass lumping. In the presence of internal damping, the problem can be reduced to a second order formulation in…
This paper is concerned about the implicit-explicit (IMEX) methods for a class of dissipative wave systems with time-varying velocity feedbacks and nonlinear potential energies, equipped with different boundary conditions. Firstly, we…
This paper develops and analyzes an optimal-order semi-discrete scheme and its fully discrete finite element approximation for nonlinear stochastic elastic wave equations with multiplicative noise. A non-standard time-stepping scheme is…
Interpolation methods for nonlinear finite element discretizations are commonly used to eliminate the computational costs associated with the repeated assembly of the nonlinear systems. While the group finite element formulation…