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Inf-sup stable nonconforming finite elements of arbitrary order on triangles. (English) Zbl 1089.65123
The main objective of this paper is to propose a consistent family of nonconforming approximations of arbitrary order \(k\) and to prove the inf-sup stability of its vector-valued version with discontinuous piecewise \(P_{k-1}\) approximations. A general convergence result for nonconforming discretisations of the stationary Stokes problem is presented with a new family of scalar nonconforming finite elements of order \(k - 1\). Also the basic property of unisolvence of the set of degrees of freedom is shown. The theoretical convergence results are confirmed by numerical experiments.

MSC:
65N30 Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs
35J25 Boundary value problems for second-order elliptic equations
65N12 Stability and convergence of numerical methods for boundary value problems involving PDEs
Software:
MooNMD
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References:
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