The smoothed finite element methods (S-FEM) are a family of methods formulated through
carefully designed combinations of the standard FEM and some of the techniques from the …

State-of-the-art finite-element methods for time-harmonic acoustics governed by the
Helmholtz equation are reviewed. Four major current challenges in the field are specifically …

The paper presents the basic ideas and the mathematical foundation of the partition of unity
finite element method (PUFEM). We will show how the PUFEM can be used to employ the …

A new finite element method is presented that features the ability to include in the finite
element space knowledge about the partial differential equation being solved. This new …

This chapter is devoted to the finite element analysis of Helmholtz problems on bounded
domains. Speaking of “Finite Element Analysis,” we elaborate on the computational analysis …

The development of numerical methods for solving the Helmholtz equation, which behaves
robustly with respect to the wave number, is a topic of vivid research. It was observed that …

The paper addresses the properties of finite element solutions for the Helmholtz equation.
The h-version of the finite element method with piecewise linear approximation is applied to …

In this paper, which is part II in a series of two, the investigation of the Galerkin finite element
solution to the Helmholtz equation is continued. While part I contained results on the h …

When using the Galerkin FEM for solving the Helmholtz equation in two dimensions, the
error of the corresponding solution differs substantially from the error of the best …

For high wave numbers, the Helmholtz equation suffers the so‐called 'pollution effect'. This
effect is directly related to the dispersion. A method to measure the dispersion on any …