Mixed and Hybrid Finite Elements

By J. Trangenstein. 2013

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Pressure-robustness and discrete Helmholtz projectors in mixed finite element methods for the incompressible Navier--Stokes equations (2016, background): “Details on the interpolation and its properties can be found in textbooks [BF91].”
On the role of the Helmholtz decomposition in mixed methods for incompressible flows and a new variational crime (2014, methodology): “In the last forty years mixed finite elements for the incompressible NavierStokes equations have seen a great success in mathematical fluid dynamics [30, 8, 43, 18, 33, 16].”
A weak Galerkin finite element method for the stokes equations (2013, unknown): “For any given ρ ∈ Wh ⊂ L 2 0(Ω), it is well known [2, 4, 5, 6, 7] that there exists a vector-valued function ṽ ∈ [H(1) 0 (Ω)] d such that (5.”
A Numerical Study on the Weak Galerkin Method for the Helmholtz Equation (2013, background): “For a given T ∈ T h , we deﬁne another vector space where ˜ P k ( T ) is the set of homogeneous polynomials of degree k and x = ( x 1 , · · · , x d ) (see [7]).”