Finite Element Methods for Maxwell's Equations

By Peter B. Monk. 2003

563 citations recorded by the source corpus.

Subfields: Computational Mechanics, Computational Theory and Mathematics, Electrical and Electronic Engineering

View Paper: https://www.semanticscholar.org/paper/e1829d90751af4d8a3b36e467567136fdaa33b1b

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Computational Mechanics

In Computational Theory and Mathematics

In Electrical and Electronic Engineering

Citations in the corpus

Finite element approximation of eigenvalue problems (2010, background): “…which makes use of the discrete compactness property and of the abstract results of Anselone (1971), was given by Monk and Demkowicz (2001) under the assumption of quasi-uniformity of the mesh (see also Ciarlet and Zou (1999), Hiptmair (2002), Monk (2003) and Costabel and Dauge (2003)).”
A dual finite element complex on the barycentric refinement (2005, methodology): “where in the second line, we used the Deny-Lions Lemma for edge elements (see Alonso-Valli [1, Formula (5.12)] and also Monk [ 24 ]) together with the reproducing polynomial property; and in the third line we simply use (18b), (18c).”
Mathematical analysis of variational isogeometric methods* (2014, methodology): “Then, due to the curl and divergence conserving properties of ι1 and ι2, respectively (see, e.g., Monk 2003, Section 3.9), the following commutative de Rham diagram is satisfied (see Hiptmair 2002, Section 2.2): R −−−−→ X̂0 ĝrad−−−−→ X̂1 ĉurl−−−−→ X̂2 d̂iv−−−−→ X̂3 −−−−→ 0 ι0 ι1 ι2 ι3 R −−−−→…”
A Survey on the Numerics and Computations for the Landau-Lifshitz Equation of Micromagnetism (2007, background): “Finite element spaces Xh and Yh are defined according to [ 53, Chapter 8 ] as N´ edelec’s first and second family of edge elements on tetrahedrons Xh = {ϕ ∈ H0(curl ,Ω out ): ϕ|K ∈P 1(K, R 3 ),”
ANALYSIS OF THE FINITE ELEMENT METHOD FOR TRANSMISSION/MIXED BOUNDARY VALUE PROBLEMS ON GENERAL POLYGONAL DOMAINS ∗ (2010, unknown): “, [4, 5, 8, 10, 20, 27, 31, 39, 45, 62, 77].”