UHML stability of a class of $ \Delta $-Hilfer FDEs via CRM

<abstract><p>We apply CRM based on an alternative FPT to investigate the approximation of a $ \Delta $-Hilfer FDE. In comparison to the Picard method, we show that the CRM has a better error estimate and economic solution.</p></abstract>

The Ostrowski inequality for $ s $-convex functions in the third sense

<abstract><p>In this paper, the Ostrowski inequality for $ s $-convex functions in the third sense is studied. By applying Hölder and power mean integral inequalities, the Ostrowski inequality is obtained for the functions, the absolute values of the powers of whose derivatives are $ s $-convex in the third sense. In addition, by means of these inequalities, an error estimate for a quadrature formula via Riemann sums and some relations involving means are given as applications.</p></abstract>

Numerical Analysis of Least-Squares Group Finite Element Method for Coupled Burgers' Problem

In this paper, a least squares group finite element method for solving coupled Burgers' problem in 2-D is presented. A fully discrete formulation of least squares finite element method is analyzed, the backward-Euler scheme for the time variable is considered, the discretization with respect to space variable is applied as biquadratic quadrangular elements with nine nodes for each element. The continuity, ellipticity, stability condition and error estimate of least squares group finite element method are proved. The theoretical results show that the error estimate of this method is . The numerical results are compared with the exact solution and other available literature when the convection-dominated case to illustrate the efficiency of the proposed method that are solved through implementation in MATLAB R2018a.

Nonconforming P1 Finite Element for the Biharmonic Problem and Its Application to Stokes Problem

The aim of this paper is to simulate the two-dimensional stationary Stokes problem. In vorticity-Stream function formulation, the Stokes problem is reduced to a biharmonic one; this approach leads to a formulation only based on the stream functions and therefore can only be applied to two-dimensional problems. The idea developed in this paper is to use the discretization of the Laplace operator by the nonconforming [Formula: see text] finite element. For the solutions which admit a regularity greater than [Formula: see text], in the general case, the convergence of the method is shown with the techniques of compactness. For solutions in [Formula: see text] an error estimate is proved, and numerical experiments are performed for the steady-driven cavity problem.

Conforming and nonconforming finite element methods for biharmonic inverse source problem

This paper deals with the numerical approximation of the biharmonic inverse source problem in an abstract setting in which the measurement data is finite-dimensional. This unified framework in particular covers the conforming and nonconforming finite element methods (FEMs). The inverse problem is analysed through the forward problem. Error estimate for the forward solution is derived in an abstract set-up that applies to conforming and Morley nonconforming FEMs. Since the inverse problem is ill-posed, Tikhonov regularisation is considered to obtain a stable approximate solution. Error estimate is established for the regularised solution for different regularisation schemes. Numerical results that confirm the theoretical results are also presented.