The effect of a sparse grad–div stabilization on control of stationary Navier–Stokes equations

Optimality Conditions of Interval-Valued Optimization Problems by Using Subdifferantials

“…Some new methods as used in vector or set optimization can be improved. Moreover, this method can also be applied to the optimal control problems in [19,20].…”

A Novel Numerical Approach for Solving Convection-Diffusion Problem with Boundary Layer Behavior

“…Here we give asymptotic estimates for the solution of continuous problem ( 1)- (2). These estimates will be used to analysis of the uniform convergence of difference approximations in the next sections.…”

“…We first show the proof of (5). Here we define the maximum principle for the problem (1)- (2). Let L be the differential operator in (1)- (2) and…”

“…Here we construct difference approximate on a uniform mesh for the problem (1)- (2). To obtain the approach of difference scheme, we will integrate equation ( 1) over ( −1 , +1 ).…”

“…Standard numerical methods for solving singularly perturbed problems are unstable and do not give accurate results due to the perturbation parameter  . If suitable numerical methods such as finite difference method and finite element method [1][2][3][4][5][6][7][8] for solving these problems are developed, then the stable and accurate results are obtained. Therefore, we prefer to apply finite difference method for this problem in this paper.…”