scholarly journals Finite element exterior calculus with script geometry

2019 ◽  
Author(s):  
Paula Cerejeiras ◽  
Uwe Kähler ◽  
Dmitrii Legatiuk
Keyword(s):  
Finite Element ◽  
Finite Element Exterior Calculus ◽  
Exterior Calculus

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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