Convergence analysis of a new multiscale finite element method for the stationary Navier–Stokes problem

A New Variational Multiscale FEM for the Steady-State Natural Convection Problem with Bubble Stabilization

“…When the solution (u L , p h , T L ) of (26) and (27) is known, we can get the solution (u h , p h , T h ) of (3) in the following way:…”

“…Then John, et al [19,20], Kaya and Rivière [21], Masud and Khurram [22], Qian et al [11] and Zheng et al [23] studied and developed variational multiscale methods. Furthermore, a new variational multiscale method with bubble stabilization for the Stokes problem was obtained by Araya et al [24], Luo et al [7] extended to solve the Navier-Stokes problem by Russo et al [4], Ge and Yan [25], and Wen and He [26]. In this paper, we shall use the new variational multiscale method (see in [4,7,24]) to solve steady-state natural convection problem with bubble stabilization.…”

Shifted Fractional-Order Jacobi Collocation Method for Solving Variable-Order Fractional Integro-Differential Equation with Weakly Singular Kernel

“…Spectral methods [39][40][41][42][43][44][45][46][47][48][49][50] have been widely adopted for solving different types of equations [51][52][53][54]. Their main goal is to approximate the solution by a finite sum of basis functions, where the coefficients are selected in order to minimize the error between the exact and approximate solutions.…”

Spectral technique for solving variable‐order fractional Volterra integro‐differential equations

“…In fact, they possess exponential rates of convergence, and reveal a high level of accuracy. We recall that the advantage of spectral numerical methods over numerical method in [48][49][50] and the method from [51][52][53] consists in its efficiency in getting a high level of accuracy. As it is known, the spectral methods are divided into four classes, namely, the Petrov-Galerkin, collocation, Galerkin, and tau methods.…”