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» A Reduced-Basis Element Method
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519views
12 years 5 months ago
The Finite Volume, Finite Difference, and Finite Elements Methods as Numerical Methods for Physical Field Problems
I. Introduction II. Foundations A. The Mathematical Structure of Physical Field Theories B. Geometric Objects and Orientation 1. Space-Time Object...
Claudio Mattiussi

Publication
289views
12 years 5 months ago
An Analysis of Finite Volume, Finite Element, and Finite Difference Methods Using Some Concepts from Algebraic Topology
In this paper we apply the ideas of algebraic topology to the analysis of the finite volume and finite element methods, illuminating the similarity between the discretization str...
Claudio Mattiussi
CORR
2010
Springer
64views Education» more  CORR 2010»
13 years 4 months ago
Dual Formulations of Mixed Finite Element Methods
Mixed finite element methods solve a PDE using two or more variables. The theory of Discrete Exterior Calculus explains why the degrees of freedom associated to the different varia...
Andrew Gillette, Chandrajit L. Bajaj
ADCM
2011
13 years 2 months ago
Approximation properties of the Generalized Finite Element Method
In this paper, we have obtained an approximation result in the Generalized Finite Element Method (GFEM) that reflects the global approximation property of the Partition of Unity ...
C. Anitescu, U. Banerjee
IFIP
2005
Springer
14 years 26 days ago
Numerical Approximation of a Control Problem for Advection-Diffusion Processes
Two different approaches are proposed to enhance the efficiency of the numerical resolution of optimal control problems governed by a linear advection– diffusion equation. In ...
Alfio Quarteroni, Gianluigi Rozza, L. Dedè,...