Abstract. Convergence of a full discretization is shown for a general class of nonlinear parabolic November 10, 2011 problems. The numerical method combines the backward Euler method for the time discretization with a generalized internal approximation scheme for the spatial discretization. The governing monotone elliptic differential operator is described by a nonlinearity that may have anisot...

A vectorial nonlocal linear hyperbolic problem with applications in superconductors of type-I is studied. The nonlocal term is represented by a (space) convolution with a singular kernel, which is arising in Eringen’s model. The well-posedness of the problem is discussed under low regularity assumptions and the error estimates for two time-discrete schemes (based on backward Euler approximation...

We consider a model of population dynamics whose mortality function is unbounded. We approximate the solution of the model using a discontinuous Galerkin finite element for the age variable and a backward Euler for the time variable. We present several numerical examples. It is experimentally shown that the scheme converges at the rate of h3/2 in the case of piecewise linear polynomial space.

An error bound is proved for a fully practical piecewise linear nite element approximation , using a backward Euler time discretization, of a model for phase separation of a multi-component alloy. Numerical experiments with three components in one and two space dimensions are also presented.

We present the semidiscrete and the backward Euler fully discrete discontinuous mixed covolume schemes for parabolic problems on triangular meshes. We give the error analysis of the discontinuous mixed covolume schemes and obtain optimal order error estimates in discontinuous H(div) and first-order error estimate in L(2).

H(div) conforming and discontinuous Galerkin (DG) methods are designed for incompressible Euler’s equation in two and three dimension. Error estimates are proved for both the semi-discrete method and fully-discrete method using backward Euler time stepping. Numerical examples exhibiting the performance of the methods are given.

For the simulation of one-dimensional ame conngurations reliable numerical tools are needed which have to be both highly eecient (large number of para-metric calculations) and at the same time accurate (in order to avoid numerical errors). This can only be accomplished using fully adaptive discretization techniques both in space and time together with a control of the discretization error. We p...

In this paper we study the convergence of the semi-implicit and the implicit Euler methods for the time integration of abstract, quasilinear hyperbolic evolution equations. The analytical framework considered here includes certain quasilinear Maxwell’s and wave equations as special cases. Our analysis shows that the Euler approximations are well-posed and convergent of order one. The techniques...

In this study, the density dependent nonlinear reactiondiffusion equation, which arises in the insect dispersal models, is solved using the combined application of differential quadrature method(DQM) and implicit Euler method. The polynomial based DQM is used to discretize the spatial derivatives of the problem. The resulting time-dependent nonlinear system of ordinary differential equations(OD...

This paper presents a case study of numerical simulations in an easy-to-use matrix computation framework named Simple Interface for Library Collections (SILC), which allows users to use various matrix computation libraries in an environmentand language-independent manner. As a practical example of numerical simulations in SILC, we selected cloth simulation based on a mass-spring model and the i...