The paper shows an inf-sup stability property for several well-known 2D and 3D Stokes elements on triangulations which are not fitted to a given smooth or polygonal domain. The property implies stability and optimal error estimates for a class of unfitted finite element methods for the Stokes and Stokes interface problems, such as Nitsche-XFEM or cutFEM. The error analysis is presented for the ...

We study finite pseudocomplemented lattices and especially those that are also complemented. With regard to the classical results on arbitrary or distributive pseudocomplemented lattices the finiteness property allows to bring significant more precise details on the structural properties of such lattices. These results can especially be applied to the lattices defined by the "weak Bruhat order"...

Piecewise affine (PWA) systems is an important class of systems. In this paper we consider optimal control of constrained, discontinuous, discrete-time, piecewise affine systems with state and input dependent disturbances. We seek to pre-compute, via dynamic programming, an explicit control law for these systems when a piecewise affine cost function is utilized. The main difficulty with this pr...

This paper restates the results on fuzzy relation equations with sup-inf composition from the viewpoint of decomposition, presents a way to describe the solution set of fuzzy relation equations, and shows a necessary and sufficient condition, which partly answers the open problem for existence of minimal solutions over complete Brouwerian lattices. Keywords— Complete Brouwerian lattice, fuzzy r...

The objective of this paper is to present a study of the solvability, stability and optimal error bounds of certain mixed finite element formulations for acoustic fluids. An analytical proof of the stability and optimal error bounds of a set of three-field mixed finite element discretizations is given, and the interrelationship between the inf–sup condition, including the numerical inf–sup test...

Let q > p > 0, and consider the Nikolskii constants Λn,p,q = inf deg(P )≤n−1 ‖P‖p ‖P‖q , where the norm is with respect to normalized Lebesgue measure on the unit circle. We prove that lim sup n→∞ n 1 p − 1 q Λp,q ≤ Ep,q , where Ep,q = inf ‖f‖Lp(R) ‖f‖Lq(R) , and the inf is taken over all entire functions f of exponential type at most π. We conjecture that the lim sup can be replaced by a limit...

The local projection method is applied to inf-sup stable discretisations of the Oseen problem. Error bounds of order r are proven for known inf-sup stable pairs of finite element spaces which approximate velocity and pressure by elements of order r and r− 1, respectively. In case of a positive reaction coefficient, the error constants are robust with respect to the viscosity but depend on the p...

When establishing and analyzing model-parameter dependent mixed formulations, it is common to consider required ellipticity and inf-sup conditions for the continuous and discrete problems. However, in the modeling of some important categories of problems, like in the analysis of plates and shells, the ellipticity condition usually considered does not naturally hold, and the inf-sup condition ca...

Convergence of mixed finite element approximations to the Stokes problem in the primitive variables is examined in maximum norm. Quasioptimal pointwise error estimates are derived for discrete spaces satisfying a weighted inf-sup condition similar to the Babuska -Brezzi condition. The usual techniques employed to prove the inf-sup condition in energy norm can be easily extended to the present s...