Upwind Based Parameter Uniform Convergence Analysis for Two Parametric Parabolic Convection Diffusion Problems by Moving Mesh Methods

Abstract

A parabolic two parametric convection-diffusion reaction problem is considered for the moving mesh error analysis. The continuous problem is discretized by the first order upwind scheme on a non uniform mesh. A curvature based error monitor function is proposed to generate the layer adapted mesh. It is proved that the numerical solution converges to the exact solution on the mesh obtained by the equidistribution of the proposed monitor function. The convergence is first order accurate. The present analysis generalizes the results obtained in earlier publications [8,9].

Numerical Solutions of a System of ODEs Based on Lie-Trotter and Strang Operator-splitting Methods

“…For one step size ∆t, we write the solution of (14) as Φ ∆t (u) = e A∆t and the solution of (15)- (16) as Ψ ∆t (u) = e C∆t e B∆t The local error is:…”

“…where A , B are noncommutative operators, Here t defines equidistant time step [14,16,18,19], and (a 0 , a 1 , ..., a m ) and (b 0 , b 1 , ..., b m ) are real numbers, that sum to unity. We apply Lie-Trotter splitting as first order splitting method, and…”