In [10, 11] D. Yu proved that on a uniform square grid the error of the finite element method is controlled by either the element residuals or the edge residuals, i.e. jumps of the normal derivative across interelement boundaries, depending on whether the degree of the finite element functions is even or odd. The proof strongly relies on the uniformity of the grid, the tensor-product structure ...

There are many applications of the least-squares finite element method for the numerical solution of partial differential equations because of a number of benefits that the leastsquares method has. However, one of most well-known drawbacks of the least-squares finite element method is the lack of exact discrete mass conservation, in some contexts, due to the fact that leastsquares method minimi...

A simple expression for the Smagorinsky length scale is derived using arguments in physical space. This expression is sensitive to the choice of the basis functions employed in a numerical method and can be used with the finite volume or the finite element method on fully unstructured grids and meshes. For a polynomial basis, the dependence of the Smagorinsky length scale on the order of comple...

An adaptive modified weak Galerkin method (AmWG) for an elliptic problem is studied in this paper, addition to its convergence and optimality. The bilinear form simplified without the need of skeletal variable, approximation space chosen as discontinuous polynomial method. Upon a reliable residual-based posteriori error estimator, algorithm proposed together with quasi-optimality proved lowest ...

In this paper, we consider the numerical solution of some nonlinear poroelasticity problems that are of Biot type and develop a general algorithm for solving nonlinear coupled systems. We discuss the difficulties associated with flow and mechanics in heterogenous media with nonlinear coupling. The central issue being how to handle the nonlinearities and the multiscale scale nature of the media....

The aim of this study is to investigatethe effective parameters on vibrations of circular cylindrical shells with fixed rotary speed andresting elastic foundation by means of analytical and finite element numerical simulation. First, the governing equations are derived using the theory of Donnell, considering the centrifugal forces,Coriolis acceleration, and the initial annular tension. Then, t...