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Error Bounds forDiscrete Geometric Approach

Lorenzo Codecasa1, Francesco Trevisan2
Politecnico di Milano, Piazza Leonardo da Vinci 32, I-20133 Milan, Italy
Università di Udine, Via delle Scienze 208, I-33100 Udine, Italy

Computer Modeling in Engineering & Sciences 2010, 59(2), 155-180. https://doi.org/10.3970/cmes.2010.059.155

Abstract

Electromagnetic problems spatially discretized by the so called Discrete Geometric Approach are considered, where Discrete Counterparts of Constitutive Relations are discretized within an Energetic Approach. Pairs of oriented dual grids are considered in which the primal grid is composed of (oblique) parallelepipeds, (oblique) triangular prisms and tetrahedra and the dual grid is obtained according to the barycentric subdivision. The focus of the work is the evaluation of the constants bounding the approximation error of the electromagnetic field; the novelty is that such constants will be expressed in terms of the geometrical details of oriented dual grids. A numerical analysis will confirm the theory.

Keywords

Cell Method, Finite Integration Technique, Discrete Counterparts of Constitutive Equations, Convergence Analysis, Error Bounds

Cite This Article

Codecasa, L., Trevisan, F. (2010). Error Bounds forDiscrete Geometric Approach. CMES-Computer Modeling in Engineering & Sciences, 59(2), 155–180.



This work is licensed under a Creative Commons Attribution 4.0 International License , which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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