We give a brief overview of stabilized finite element methods and illustrate the developments applied to the advection-diffusion equation.

Adaptive methods are now widely used in the scientific computation to achieve better accuracy with minimum degree of freedom. In this chapter, we shall briefly survey recent progress on the convergence analysis of adaptive finite element methods (AFEMs) for second order elliptic partial differential equations and refer to Nochetto, Siebert and Veeser [14] for a detailed introduction to the theo...

Finite element methods in which two spaces are used to approximate two different variables receive the general denomination of mixed methods. In some cases, the second variable is introduced in the formulation of the problem because of its physical interest and it is usually related with some derivatives of the original variable. This is the case, for example, in the elasticity equations, where...

The aim of present study is to investigate the effect of various parameters such as length, thickness, density, shear modulus of the core and Young modulus of skins for various boundary conditions:  clamped-free and simply supported. By applying the model of Khalili et al for frees vibration analysis of sandwich beams by using finite element methods. Where, the core density is taken on consider...

The mortar finite element is an example of a non-conforming method which can be used to decompose and re-compose a domain into subdomains without requiring compatibility between the meshes on the separate components. We obtain stability and convergence results for this method that are uniform in terms of both the degree and the mesh used, without assuming quasiuniformity for the meshes. Our res...