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A Posteriori Error Estimates For Maxwell's Equations Using Auxiliary Subspace Techniques, Ahmed El Sakori

Dissertations and Theses

The aim of our work is to construct provably efficient and reliable error estimates of discretization error for Nédélec (edge) element discretizations of Maxwell's equations on tetrahedral meshes. Our general approach for estimating the discretization error is to compute an approximate error function by solving an associated problem in an auxiliary space that is chosen so that:

-Efficiency and reliability results for the computed error estimates can be established under reasonable and verifiable assumptions.

-The linear system used to compute the approximate error function has condition number bounded independently of the discretization parameter.

In many applications, it is some functional …

Maxwell's Equations And Yang-Mills Equations In Complex Variables : New Perspectives, Sachin Munshi

Legacy Theses & Dissertations (2009 - 2024)

Maxwell's equations, named after James C. Maxwell, are a U(1) gauge theory describing the interactions between electric and magnetic fields. They lie at the heart of classical electromagnetism and electrodynamics. Yang-Mills equations, named after C. N. Yang and Robert Mills, generalize Maxwell's equations and are associated with a non-abelian gauge theory called Yang-Mills theory. Yang-Mills theory unified the electroweak interaction with the strong interaction (QCD), and it is the foundation of the Standard Model in particle physics.

Remark On Lehnert’S Revised Quantum Electrodynamics (Rqed) As An Alternative To Francesco Celani’S Et Al. Maxwell-Clifford Equations: With An Outline Of Chiral Cosmology Model And Its Role To Cmns, Florentin Smarandache, Victor Christianto, Yunita Umniyati

Branch Mathematics and Statistics Faculty and Staff Publications

In a recent paper published in JCMNS in 2017, Francesco Celani, Di Tommaso & Vassalo argued that Maxwell equations rewritten in Clifford algebra are sufficient to describe the electron and also ultra-dense deuterium reaction process proposed by Homlid et al. Apparently, Celani et al. believed that their Maxwell-Clifford equations are an excellent candidate to surpass both Classical Electromagnetic and Zitterbewegung QM. Meanwhile, in a series of papers, Bo Lehnert proposed a novel and revised version of Quantum Electrodynamics (RQED) based on Proca equations. Therefore, in this paper, we gave an outline of Lehnert’s RQED, as an alternative framework to Celani …