We study the spatially semidiscrete lumped mass method for the model homogeneous heat equation with homogeneous Dirichlet boundary conditions. Improving earlier results we show that known optimal order smooth initial data error estimates for the standard Galerkin method carry over to the lumped mass method whereas nonsmooth initial data estimates require special assumptions on the triangulation...

In the current research with novel first and second differentiations of a yield function, Euler forward along with Euler backward with its consistent elastic-plastic modulus are newly implemented in finite element program in rate-independent plasticity. An elastic-plastic internally pressurized thick walled cylinder is analyzed with four famous criteria including both pressure dependent and ind...

Singularly perturbed parabolic differential problems with non-smooth data and a large negative shift in the space variable were studied. The proposed scheme is based on method of lines, nonstandard finite difference for discretization, followed by backward Euler resulting system initial value time discretization. stability uniform convergence are investigated proved. As demonstrated theoretical...

In this paper, we deal with a singularly perturbed parabolic convection-diffusion problem. Shishkin mesh and hybrid third-order finite difference scheme are adopted for the spatial discretization. Uniform backward Euler used temporal Furthermore, preconditioning approach is also to ensure uniform convergence. Numerical experiments show that method first-order accuracy in time almost space.

In this paper we study the stability for all positive time of the fully implicit Euler scheme for the two-dimensional Navier–Stokes equations. More precisely, we consider the time discretization scheme and with the aid of the discrete Gronwall lemma and the discrete uniform Gronwall lemma we prove that the numerical scheme is stable.

we derive error estimates in the appropriate norms, for the streamlinediffusion (sd) finite element methods for steady state, energy dependent,fermi equation in three space dimensions. these estimates yield optimal convergencerates due to the maximal available regularity of the exact solution.high order sd method together with implicit integration are used. the formulationis strongly consistent...

We consider the simulation of a system decoupled forward–backward stochastic differential equations (FBSDEs) driven by pure jump Lévy process L and an independent Brownian motion B . allow to have infinite activity. Therefore, it is necessary for employ finite approximation its measure. use generalized shot noise series representation method [26] approximate driving compute p error, ≥ 2, betwee...

This paper examines stability analysis of two classes of improved backward Euler methods, namely split-step $(theta, lambda)$-backward Euler (SSBE) and semi-implicit $(theta,lambda)$-Euler (SIE) methods, for nonlinear neutral stochastic delay differential equations (NSDDEs). It is proved that the SSBE method with $theta, lambdain(0,1]$ can recover the exponential mean-square stability with some...

We show that the Euler-discretization of nonlinear continuous-time model a single mast stacker crane is flat. The construction flat output based on transformation subsystem into linear time-variant discrete-time controller canonical form. Based derived output, which also function backward-shifts system variables, we discuss planning trajectories to achieve transition between two rest positions ...

<p style='text-indent:20px;'>We study a continuous data assimilation (CDA) algorithm for velocity-vorticity formulation of the 2D Navier-Stokes equations in two cases: nudging applied to velocity and vorticity, only. We prove that under typical finite element spatial discretization backward Euler temporal discretization, application CDA preserves unconditional long-time stability property...