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NOTES.md

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Literature

Glitter

... and Glitterati.

DA

L u == ρ
B d u == 0

d u - f == 0
δ f == ρ
B f == 0

Can we rewrite this without δ or ⋆?

  • DA: need to remove harmonic forms from f: P(1-H) f. only for strong form?

  • DA: R[u]=0: von Neumann bc R[u]=D-1: Dirichlet bc

  • DA: mixed weak formulations have no hodge dual

  • magnetic bc: R=1   (or R=2?)
    
  • electric bc: R=2   (or R=1?)
    
  • DA: Hodge Laplacian is always well posed! choose complexes (and respective basis functions), then solve in the discrete with the same mixed weak formulation.

  • DA: trace is projection onto boundary; trace maps D-dim form onto (D-1)-dim form

  • DA: 0-forms: naturally piecewise continuous (FE), polynomial D-forms: naturally piecewise discontinuous (DG), polynomial - DOFs need to be located on either of vertices, edges, faces, etc. - must be unisolvent (be a basis?)