scholarly journals Local L2-bounded commuting projections in FEEC

2021 ◽  
Author(s):  
Douglas Arnold ◽  
Johnny Guzmán
Keyword(s):  
Finite Element ◽  
Exterior Derivative ◽  
Finite Element Exterior Calculus ◽  
Exterior Calculus ◽  
Local Projections

We construct local projections into canonical finite element spaces that appear in the finite element exterior calculus. These projections are bounded in L2 and commute with the exterior derivative.

Mimetic Interpolation of Vector Fields on Arakawa C/D Grids

2019 ◽  
Vol 147 (1) ◽  
pp. 3-16
Author(s):  
Alexander Pletzer ◽  
Wolfgang Hayek
Keyword(s):  
Finite Element ◽  
Vector Fields ◽  
Total Flux ◽  
Machine Accuracy ◽  
Weighted Interpolation ◽  
Discretization Methods ◽  
Finite Element Exterior Calculus ◽  
Interpolation Methods ◽  
Discrete Exterior Calculus ◽  
Exterior Calculus

Interpolation methods for vector fields whose components are staggered on horizontal Arakawa C or D grids are presented. The interpolation methods extend bilinear and area-weighted interpolation, which are widely used in Earth sciences, to work with vector fields (essentially discretized versions of differential 1-forms and 2-forms). The interpolation methods, which conserve the total flux and enforce Stokes’ theorem to near-machine accuracy, are a natural complement to discrete exterior calculus and finite element exterior calculus discretization methods.

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