Trigonometric function used to formulate a multi-nodal finite tubular element

A C1-p2 Finite Element without Nodal Basis

A new finite element, which is continuously differentiable, but only piecewise quadratic polynomials on a type of uniform triangulations, is introduced. We construct a local basis which does not involve nodal values nor derivatives. Different from the traditional finite elements, we have to construct a special, averaging operator which is stable and preserves quadratic polynomials. We show the ...

Multi - Level Finite Element

Fast Finite Element Method Using Multi-Step Mesh Process

This paper introduces a new method for accelerating current sluggish FEM and improving memory demand in FEM problems with high node resolution or bulky structures. Like most of the numerical methods, FEM results to a matrix equation which normally has huge dimension. Breaking the main matrix equation into several smaller size matrices, the solving procedure can be accelerated. For implementing ...

Non-overlapping Domain Decomposition Method and Nodal Finite Element Method

The non-overlapping domain decomposition method is an efficient approach for solving time harmonic scattering wave problems. It is used here to reduce large size systems solution to that of several systems of small size and to construct efficient procedures to couple finite element and boundary element methods. The lack of a satisfactory treatment of the so-called cross-points, nodes being shar...

A Few Finite Trigonometric Sums

Finite trigonometric sums occur in various branches of physics, mathematics, and their applications. These sums may contain various powers of one or more trigonometric functions. Sums with one trigonometric function are known; however, sums with products of trigonometric functions can become complicated, and may not have a simple expression in a number of cases. Some of these sums have interest...