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...

In the numerical solution of practical problems of physics or engineering such as, e.g., computational fluid dynamics, elasticity, or semiconductor device simulation one often encounters the difficulty that the overall accuracy of the numerical approximation is deteriorated by local singularities such as, e.g., singularities arising from re-entrant corners , interior or boundary layers, or shar...

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

By using the finite element $p$-Version in convection-diffusion problems, we can attain to a stabilized and accurate results. Furthermore, the fundamental of the finite element $p$-Version is augmentation degrees of freedom. Based on the fact that the finite element and the meshless methods have similar concept, it is obvious that many ideas in the finite element can be easily used in the meshl...