We propose an analysis for the stabilized finite element methods proposed in [2] valid in the case of ill-posed problems for which only weak continuous dependence can be assumed. A priori and a posteriori error estimates are obtained without assuming coercivity or inf-sup stability of the continuous problem. Résumé Estimations d’erreurs pour des méthodes d’éléments finis stabilisées appliquées ...

In this paper, we consider the discretization of the Stokes problem on domain partitions with non-matching meshes. We propose a hybrid mortar method, which is motivated by a variational characterization of solutions of the corresponding interface problem. For the discretization of the subdomain problems, we utilize standard inf-sup stable finite element pairs. The introduction of additional unk...

Heavy doped n-type β-Ga 2 O xmlns:xlink="http://www.w3.org/1999/xlink">3 (HD-Ga ) was obtained by employing Si ion implantation technology on unintentionally single crystal substrates. To repair the Ga lattice damage and activate after implantation, implanted substrates were annealed at 95...

This paper is the second part of a two-part paper treating a non-selfadjoint quadratic eigenvalue problem for the linear stability of solutions to the Taylor-Couette problem for flow of a viscous liquid in a deformable cylinder, with the cylinder modelled as a membrane. The first part formulated the problem, analyzed it, and presented computations. In this second part, we first give a weak form...

Parametric Partial Differential Equations arise in many areas of applied mathematics and the natural sciences. Efficient numerical simulations to these types of problems across a wide range of parameter values presents a stiff computational challenge. The Reduced Basis Method presents an efficient scheme for solving these types of problem. Utilization of this method however, depends on the know...

We present an approach to the construction of lower bounds for the coercivity and inf-sup stability constants required in a posteriori error analysis of reduced basis approximations to affinely parametrized partial differential equations. The method, based on an Offline-Online strategy relevant in the reduced basis many-query and real-time context, reduces the Online calculation to a small Line...

We present a method for mass proofs of theorems of certain forms in a formal theory of fuzzy relations and classes. The method is based on formal identification of fuzzy classes and inner truth values with certain fuzzy relations, which allows transferring basic properties of sup-T and inf-R compositions to a family of more than 30 composition-related operations, including sup-T and inf-R image...

For the Stokes problem in a twoor three-dimensional bounded domain, we propose a new mixed finite element discretization which relies on a nonconforming approximation of the velocity and a more accurate approximation of the pressure. We prove that the velocity and pressure discrete spaces are compatible, in the sensé that they satisfy an inf-sup condition of Babuska and Brezzi type, and we déri...