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Inf-sup nonconforming finite elements of higher order on quadrilaterals and hexahedra. (English) Zbl 1147.65094
The author presents the discretisation of the Stokes problem
\[ \Delta u +\nabla p = f \quad \text{in }\Omega, \qquad \operatorname{div} u = 0 \quad \text{in }\Omega, \qquad u = g \quad \text{on }\partial\Omega, \] using two systems of finite elements constructed on the quadrilaterals if \( \Omega\subset \mathbb R ^{2}\) and on hexahedra in the case when \( \Omega\subset\mathbb R ^{3}\). The construction of finite elements uses the one-dimensional Legendre polynomials. The numerical results show only the error of the solution for two concrete examples.

MSC:
65N30 Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs
65N15 Error bounds for boundary value problems involving PDEs
35J25 Boundary value problems for second-order elliptic equations
35Q30 Navier-Stokes equations
Software:
MooNMD
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References:
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