A truly general and systematic theory of finite element methods (FEM) should be formulated
using, as trial and test functions, piecewise‐defined functions that can be fully discontinuous …

Because the complete set of Trefftz functions for the 3D biharmonic equation is not yet well
established, a multiple-direction Trefftz method (MDTM) and an in-plane biharmonic …

In this paper we numerically solve both the direct and the inverse Cauchy problems of
biharmonic equation by using a multiple-scale Trefftz method (TM). The approximate …

In recent years, new and more effective procedures for applying collocation have been
published. This article is devoted to present a revision of this subject and complement its …

Abstract Domain decomposition methods (DDM) have received much attention in recent
years. They constitute the most effective means of using parallel computing resources to …

The hybrid-Trefftz formulation of the finite element method is applied to the transient,
physically and geometrically linear analysis of incompressible saturated porous media. Two …

Abstract An Alternating Directions Implicit method is presented to solve the homogeneous
heat diffusion equation when the governing equation is a bi-harmonic equation (X) based on …

Los objetivos generales de este trabajo fueron, primero, desarrollar con detalle el modelo
numérico de Método de Elemento Finito con Funciones Óptimas (FEM-OF por sus siglas en …

This chapter shows the application of the Trefftz-Herrera collocation method [1-3] to obtain
the numerical solution of nonstandard boundary value problems with prescribed jumps …

I want to thank the editors, for having invited me to write this Introductory Chapter, whose
initial intention was to give a historical background of Mathematical and Computational …