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.

This paper proposes semi-discrete and fully discrete hybridizable discontinuous Galerkin (HDG) methods for the Burgers' equation in two three dimensions. In spatial discretization, we use piecewise polynomials of degrees $ k \ (k \geq 1), k-1 l (l = k-1; k) to approximate scalar function, flux variable interface trace respectively. full discretization method, apply a backward Euler scheme tempo...

We propose a numerical approximation method for the Cahn-Hilliard equations that incorporates continuous data assimilation in order to achieve long time accuracy. The uses C0 interior penalty spatial discretization of fourth equations, together with backward Euler temporal discretization. prove is stable and accurate, arbitrarily inaccurate initial conditions, provided enough measurements are i...

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...

A discretization of an optimal control problem a stochastic parabolic equation driven by multiplicative noise is analyzed. The state discretized the continuous piecewise linear element method in space and backward Euler scheme time. convergence rate $$ O(\tau ^{1/2} + h^2) rigorously derived.

Dynamical systems can often be decomposed into loosely coupled subsystems. The system of ordinary differential equations (ODEs) modelling such a problem can then be partitioned corresponding to the subsystems, and the loose couplings can be exploited by special integration methods to solve the problem using a parallel computer or just solve the problem more efficiently than by standard methods....

A nonlinear degenerate convection-diffusion initial boundary value problem is studied in a bounded domain. A dynamical boundary condition (containing the time derivative of a solution) is prescribed on the one part of the boundary. This models a non-perfect contact on the boundary. Existence and uniqueness of a weak solution in corresponding function spaces is proved using the backward Euler me...

A fully discrete penalty finite element method is presented for the two-dimensional time-dependent Navier-Stokes equations. The time discretization of the penalty Navier-Stokes equations is based on the backward Euler scheme; the spatial discretization of the time discretized penalty Navier-Stokes equations is based on a finite element space pair (Xh,Mh) which satisfies some approximate assumpt...

This work develops adaptive time stepping algorithms for the approximation of a functional of a diffusion with jumps based on a jump augmented Monte Carlo Euler–Maruyama method, which achieve a prescribed precision. The main result is the derivation of new expansions for the time discretization error, with computable leading order term in a posteriori form, which are based on stochastic flows a...

We study the error induced by the time discretization of a decoupled forwardbackward stochastic differential equations (X,Y,Z). The forward component X is the solution of a Brownian stochastic differential equation and is approximated by a Euler scheme XN with N time steps. The backward component is approximated by a backward scheme. Firstly, we prove that the errors (Y N −Y,ZN −Z) measured in ...