Second Order Convergence of a Modified MAC Scheme for Stokes Interface Problems

Convergence of the MAC Scheme for the Compressible Stokes Equations

Abstract. We prove in this paper the convergence of the Marker and Cell (MAC) scheme for the discretization of the steady state compressible Stokes equations on two or three dimensional Cartesian grids. Existence of a solution to the scheme is proven, followed by estimates on approximate solutions, which yield the convergence of the approximate solutions, up to a subsequence, and in an appropri...

Convergence Analysis of a Second Order Convex Splitting Scheme for the Modified Phase Field Crystal Equation

In this paper we provide a detailed convergence analysis for an unconditionally energy stable, second order accurate convex splitting scheme for the modified phase field crystal equation, a generalized damped wave equation for which the usual phase field crystal equation is a special degenerate case. The fully discrete, fully second order finite difference scheme in question was derived in a re...

A second-order positivity preserving scheme for semilinear parabolic problems

In this paper we study the convergence behaviour and geometric properties of Strang splitting applied to semilinear evolution equations. We work in an abstract Banach space setting that allows us to analyse a certain class of parabolic equations and their spatial discretizations. For this class of problems, Strang splitting is shown to be stable and second-order convergent. Moreover, it is show...

L ∞ - convergence of saddle - point approximations for second order problems

Design of a Model Reference Adaptive Controller Using Modified MIT Rule for a Second Order System

Sometimes conventional feedback controllers may not perform well online because of the variation in process dynamics due to nonlinear actuators, changes in environmental conditions and variation in the character of the disturbances. To overcome the above problem, this paper deals with the designing of a controller for a second order system with Model Reference Adaptive Control (MRAC) scheme usi...