Abstract
A framework to systematically decouple high order elliptic equations into a combination of Poisson-type and Stokes-type equations is developed. The key is to systematically construct the underling ...
Highlights
We shall develop a framework to systematically decouple high order elliptic equations into combination of Poisson-type and Stokes-type equations
Differential complexes and corresponding Helmholtz decompositions play the fundamental role in the design and analysis of mixed finite element methods
The generalized Helmholtz decomposition of Banach spaces presented in this paper can be regarded as a generalization of the well-known Helmholtz-Hodge decomposition in [4]
Summary
We shall develop a framework to systematically decouple high order elliptic equations into combination of Poisson-type and Stokes-type equations. Differential complex, commutative diagram, Helmholtz decomposition, mixed formulation, decoupling, discretization When the quotient space ker( ̃d1)/ ̃d2(W ) is non-trivial, i.e., the sequence (2.1) is not exact, the Helmholtz decomposition will be
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