Abstract We analyze backward Euler time stepping schemes for a primal DPG formulation of class parabolic problems. Optimal error estimates are shown in natural norm and the L 2 {L^{2}} field variable. For heat equation solution our equals standard Galerkin scheme and, thus, optimal bound...

The paper presents a simple but efficient new numerical scheme for the integration of nonlinear constitutive equations. Although it can be used for integration of system of algebraic and differential equations in general, the scheme is primarily developed for use with direct solution methods for solving boundary value problems, e.g. explicit dynamic analysis in ABAQUS/Explicit. In the developed...

In this paper, the stability and accuracy properties of exponentially-t integration algorithms applied to the test problem x= ?Ax are compared to the more standard backward-Euler and semi-implicit methods. For the analysis, A 2 R nn is assumed to be connectedly diagonally-dominant with positive diagonals, as this models the equations resulting from the way MOS transistors and interconnect paras...

which is uniform with respect to λ > 0. Recall that we showed that this stability estimate is preserved by the implicit Euler method. However, the explicit Euler method is only stable provided that ∆t < 2/λ, so its stability is not uniform in λ. One consequence is that it is less efficient to compute with the explicit Euler method over long time intervals. Note that in this example, we also hav...

Abstract. In this paper, a linearized backward Euler method is discussed for the equations of motion arising in the Oldroyd model of viscoelastic fluids. Some new a priori bounds are obtained for the solution under realistically assumed conditions on the data. Further, the exponential decay properties for the exact as well as the discrete solutions are established. Finally, a priori error estim...

We consider the stochastic Allen-Cahn equation perturbed by smooth additive Gaussian noise in a spatial domain with smooth boundary in dimension d ≤ 3, and study the semidiscretization in time of the equation by an implicit Euler method. We show that the method converges pathwise with a rate O(∆tγ) for any γ < 1 2 . We also prove that the scheme converges uniformly in the strong Lp-sense but wi...

This article deals with some generalizations of the Cahn–Hilliard equation mass source endowed Neumann boundary conditions. This has many applications in real life e.g. biology and image inpainting. The first part this article, discusses stationary problem source. We prove existence a unique solution associated problem. Then, latter we consider evolution construct n...