We provide a systematic way to design computable bilinear forms which, on theclass of subspaces W* V' that can be obtained by duality from a given finite dimensional subspaceW of an Hilbert space V, are spectrally equivalent to the scalar product of V'. In the spirit ofBaiocchi-Brezzi (1993) and Bertoluzza (1998), such bilinear forms can be used to build a stabilizeddiscretization algorithm for the solution of an abstract saddle point problem allowing to decouple, inthe choice of the discretization spaces, the requirements related to the approximation from the onesrelated to the inf-sup compatibility condition, which, however, can not be completely avoided.
Algebraic representation of dual scalar products and stabilization of saddle point problems
S Bertoluzza
2021
Abstract
We provide a systematic way to design computable bilinear forms which, on theclass of subspaces W* V' that can be obtained by duality from a given finite dimensional subspaceW of an Hilbert space V, are spectrally equivalent to the scalar product of V'. In the spirit ofBaiocchi-Brezzi (1993) and Bertoluzza (1998), such bilinear forms can be used to build a stabilizeddiscretization algorithm for the solution of an abstract saddle point problem allowing to decouple, inthe choice of the discretization spaces, the requirements related to the approximation from the onesrelated to the inf-sup compatibility condition, which, however, can not be completely avoided.| File | Dimensione | Formato | |
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Descrizione: Algebraic representation of dual scalar products and stabilization of saddle point problems
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