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Maxwell curl-energy Ritz projection

Definition

Assume Countable Choice in the inherited edge/face finite-element space branch. Let $V = H_{0} (curl; Ω)$ with the PEC convention in Edge-face Maxwell finite element semidiscretization, and let $V_{h} = N_{h}^{1} \cap H_{0} (curl; Ω)$ . Define $m (u, v) = \int_{Ω} v^{T} ϵ u d x, a (u, v) = \int_{Ω} (curl v)^{T} μ^{- 1} curl u d x, a_{+} (u, v) = m (u, v) + a (u, v) .$ For $u \in V$ , the Maxwell curl-energy Ritz projection $R_{h} u \in V_{h}$ is the solution of $a_{+} (R_{h} u, v_{h}) = a_{+} (u, v_{h}) (v_{h} \in V_{h}) .$ Its finite-dimensional well-definedness, orthogonality, and best-approximation property are supplied by Well-definedness and best approximation of the Maxwell Ritz map ↗.

Depends on

Used by

Dependency tree · two levels

11 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

Long Chen, Finite Element Methods for Maxwell Equations, complete lecture notes (standard reference, not scraped)
Peter Monk, Mathematical and Numerical Analysis of Maxwell’s Equations, complete lecture notes (standard reference, not scraped)