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Zero tangential trace H(curl) space
Definition
Let be open and set where the norm is that of The real H(curl) graph space on a polyhedron. This is the closure-defined zero-tangential subspace used on this page. Identifying this closure with the full kernel of a particular boundary trace map is not part of the definition.
Remarks
On a bounded Lipschitz polyhedron admitting a finite matching affine tetrahedral mesh, every member has zero weak tangential trace in the trace-quotient sense of Weak tangential trace on a Lipschitz polyhedron.
Depends on
Used by
- Edge-face Maxwell finite element semidiscretization Definition
- PEC Maxwell cavity eigenproblem and full-kernel gauge Definition
- Transient Maxwell system with piecewise materials and boundary conditions Definition
- A repeated unit-cube Maxwell eigenvalue cluster Example
- A topological PEC zero mode on a spherical shell Example
- An explicit PEC standing wave in the unit cube Example
- A bounded regular decomposition with both summands satisfying full Dirichlet conditions Lemma
- Averaged pullback Whitney moments and uniform near identity Lemma
- Compact embedding and curl Poincare inequality for the continuous PEC quotient Lemma
- Kernel projection gives dense conforming gauge approximants Lemma
- Smooth fields are approximated by the lowest-order edge family Lemma
- Weak graph limits preserve zero tangential H(curl) Lemma
- Weak tangential trace on a Lipschitz polyhedron Lemma
- Whole-space support and the zero-boundary Sobolev closure Lemma
- Regular decomposition of zero-tangential H(curl) fields Theorem
- Smooth PEC edge finite element Maxwell error from compatible projections Theorem
- Spectral convergence and no nonzero pollution for PEC edge elements Theorem
- Uniformly bounded commuting projection for lowest-order Nedelec spaces Theorem
Dependency tree · two levels
10 results within two dependency steps of this one, each drawn at its shortest distance from it. An arrow runs from a result to what uses it, so the chart reads left to right and ends at this result, which carries a heavier outline. Every node is a link to that result. Click elsewhere on the chart to enlarge it.
Sources
- Ralf Hiptmair and Clemens Pechstein, Regular Decompositions of Vector Fields—Continuous, Discrete, and Structure-Preserving (standard reference, not scraped)