Unified formulation of numerical methods

Unified theory of Trefftz methods and numerical implications

In the 1 International Workshop, devoted to Trefftz Method, the author presented an indirect approach to Trefftz Method (Trefftz-Herrera Method), while in the Second one some of the basic ideas of how to integrate different approaches to Trefftz method were introduced. The present Plenary Lecture, corresponding to the 3 International Workshop of this series, is devoted to show that Trefftz Meth...

Numerical Methods in a Unified Object-Oriented Approach

Four-component relativistic theory for NMR parameters: unified formulation and numerical assessment of different approaches.

Several four-component relativistic approaches for nuclear magnetic shielding constant have recently been proposed and their formal relationships have also been established [Xiao et al., J. Chem. Phys. 126, 214101 (2007)]. It is shown here that the approaches can be recast into a unified form via the generic ansatz of orbital decomposition. The extension of the formalisms to magnetizability (an...

A Unified Formulation of Nuclear Fluctuation Theory

The statistical theory of fluctuations was initiated by ERICSON 1 in 1960 in the appendix of his review article on the statistical model of the compound nucleus. This was at a time when nuclear fluctuations had not yet been observed or recognized as such in scattering experiments. ERICSON pointed out that the excitation functions and angular distributions of nuclear reactions involving a compou...

Unified primal formulation-based a priori and a posteriori error analysis of mixed finite element methods

We derive in this paper a unified framework for a priori and a posteriori error analysis of mixed finite element discretizations of second-order elliptic problems. It is based on the classical primal weak formulation, the postprocessing of the potential proposed in [T. Arbogast and Z. Chen, On the implementation of mixed methods as nonconforming methods for secondorder elliptic problems, Math. ...