Singularities of Electromagnetic Fields¶in Polyhedral Domains

By Martin Costabel, Monique Dauge. 2000

372 citations recorded by the source corpus.

Subfields: Computational Mechanics, Computational Theory and Mathematics, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/74f22ffe73af4b25ec6e1ca088b1a38d5934ff5c

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In Computational Mechanics

In Computational Theory and Mathematics

In Mathematical Physics

Citations in the corpus

A mixed finite element method with exactly divergence-free velocities for incompressible magnetohydrodynamics (2010, background): “However, since the strongest magnetic singularities have regularity below H(1), straightforwardly applied nodal elements may fail to resolve them in non-convex polyhedral domains; see [15] and the references therein.”
ANALYSIS OF THE FINITE ELEMENT METHOD FOR TRANSMISSION/MIXED BOUNDARY VALUE PROBLEMS ON GENERAL POLYGONAL DOMAINS ∗ (2010, background): “This distinction will be achieved by considering the connected neighborhoods of B(x, r) ∩ Ω, when x is on the boundary, as in Dauge [32].”
Forty Years of the Crouzeix‐Raviart element (2015, background): “Therefore all conforming finite element methods based on this formulation would fail unless u ∈ [H (1)( )]2, which is in general not true if is nonconvex [124].”
High‐order continuous and discontinuous Galerkin methods for wave problems (2013, background): “In addition, as usually in the presence of non-smooth boundaries such as corners, the solution of the wave equation is singular leading to non-optimal convergence both for h and p-refinement, see for instance [44,45].”
Well-posedness and Regularity for the Elasticity Equation with Mixed Boundary Conditions on Polyhedral Domains and Domains with Cracks (2010, background): “See also [3, 5, 16, 18, 23, 38, 39, 49, 56], to mention just a few papers.”
Residual based a posteriori error estimators for eddy current computation (2000, neutral): “Since the fields feature strong singularities at reentrant corners [31] and at irregular material interfaces [32], a higher resolution of the mesh in these zones is desirable.”
A hinged plate equation and iterated Dirichlet Laplace operator on domains with concave corners (2007, neutral): “For the study of corner singularities for the (time-harmonic) Maxwell equations, that is, for ∇ × E − iωμH = 0 and ∇ × H + iωεE = J, we refer to [5,9] and also to [1,7,8].”