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DIVERGENCE-FREE FINITE ELEMENTS ON TETRAHEDRAL GRIDS FOR k ≥ 6

ZHANG, SHANGYOU

Mathematics of computation, 2011-04, Vol.80 (274), p.669-695 [Periódico revisado por pares]

Providence, RI: American Mathematical Society

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Título:
DIVERGENCE-FREE FINITE ELEMENTS ON TETRAHEDRAL GRIDS FOR k ≥ 6
Autor: ZHANG, SHANGYOU
Assuntos: Airy equation ; Cubes ; Degrees of freedom ; Exact sciences and technology ; Finite element method ; Interpolation ; Mathematics ; Methods of scientific computing (including symbolic computation, algebraic computation) ; Numerical analysis ; Numerical analysis. Scientific computation ; Penalty function ; Polynomials ; Sciences and techniques of general use ; Tetrahedrons ; Triangles ; Vertices
É parte de: Mathematics of computation, 2011-04, Vol.80 (274), p.669-695
Descrição: It was shown two decades ago that the P k -P k-1 mixed element on triangular grids, approximating the velocity by the continuous P k piecewise polynomials and the pressure by the discontinuous P k-1 piecewise polynomials, is stable for all k ≥ 4, provided the grids are free of a nearly-singular vertex. The problem with the method in 3D was posted then and remains open. The problem is solved partially in this work. It is shown that the P k -P K-1 element is stable and of optimal order in approximation, on a family of uniform tetrahedral grids, for all K > 6. The analysis is to be generalized to non-uniform grids, when we can deal with the complicity of 3D geometry. For the divergence-free elements, the finite element spaces for the pressure can be avoided in computation, if a classic iterated penalty method is applied. The finite element solutions for the pressure are computed as byproducts from the iterate solutions for the velocity. Numerical tests are provided.
Editor: Providence, RI: American Mathematical Society
Idioma: Inglês

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DIVERGENCE-FREE FINITE ELEMENTS ON TETRAHEDRAL GRIDS FOR k ≥ 6

ZHANG, SHANGYOU

Providence, RI: American Mathematical Society

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