Search results for "Backward Euler method"
showing 5 items of 5 documents
ATTRACTORS FOR A LATTICE DYNAMICAL SYSTEM GENERATED BY NON-NEWTONIAN FLUIDS MODELING SUSPENSIONS
2010
In this paper we consider a lattice dynamical system generated by a parabolic equation modeling suspension flows. We prove the existence of a global compact connected attractor for this system and the upper semicontinuity of this attractor with respect to finite-dimensional approximations. Also, we obtain a sequence of approximating discrete dynamical systems by the implementation of the implicit Euler method, proving the existence and the upper semicontinuous convergence of their global attractors.
Analysis of a Parabolic Cross-Diffusion Semiconductor Model with Electron-Hole Scattering
2007
The global-in-time existence of non-negative solutions to a parabolic strongly coupled system with mixed Dirichlet–Neumann boundary conditions is shown. The system describes the time evolution of the electron and hole densities in a semiconductor when electron-hole scattering is taken into account. The parabolic equations are coupled to the Poisson equation for the electrostatic potential. Written in the quasi-Fermi potential variables, the diffusion matrix of the parabolic system contains strong cross-diffusion terms and is only positive semi-definite such that the problem is formally of degenerate type. The existence proof is based on the study of a fully discretized version of the system…
Zero Viscosity Limit for Analytic Solutions, of the Navier-Stokes Equation on a Half-Space.¶I. Existence for Euler and Prandtl Equations
1998
This is the first of two papers on the zero-viscosity limit for the incompressible Navier-Stokes equations in a half-space. In this paper we prove short time existence theorems for the Euler and Prandtl equations with analytic initial data in either two or three spatial dimensions. The main technical tool in this analysis is the abstract Cauchy-Kowalewski theorem. For the Euler equations, the projection method is used in the primitive variables, to which the Cauchy-Kowalewski theorem is directly applicable. For the Prandtl equations, Cauchy-Kowalewski is applicable once the diffusion operator in the vertical direction is inverted.
On numerical simulation of the continuous casting process
1988
In this paper a steady-state nonlinear parabolic-type model, which simulates the multiphase heat transfer during solidification in continuous casting, is presented. An enthalpy formulation is used and we apply a FE-method in space and an implicit Euler method in time. A detailed solution algorithm is presented. We compute the temperature distributions in the strand when the boundary conditions (mold/spray cooling) on the strand surface are known. The numerical model gives thereby a good basis for the testing of new designs of continuous-casting machines. An application of the model to continuous casting of billets is presented.
DEGENERATE MATRIX METHOD FOR SOLVING NONLINEAR SYSTEMS OF DIFFERENTIAL EQUATIONS
1998
Degenerate matrix method for numerical solving nonlinear systems of ordinary differential equations is considered. The method is based on an application of special degenerate matrix and usual iteration procedure. The method, which is connected with an implicit Runge‐Kutta method, can be simply realized on computers. An estimation for the error of the method is given. First Published Online: 14 Oct 2010