Least-squares finite element methods / Pavel B. Bochev, Max D. Gunzburger

Auteur: Bochev, Pavel B. - AuteurCo-auteur: Gunzburger, Max D. - AuteurType de document: Livre numériqueCollection: Applied mathematical sciences ; 166Langue: anglaisÉditeur: New York : Springer, 2009 ISBN: 9780387308883 Note: ... Recent results that are incorporated in the book, refer in particular to negative norm least-squares finite element methods. Note that least-squares formulations refer to the target spaces of the (systems of) differential operators, and minimal regularity leads often to negative norms. In contrast to this fact, the finite element method and the bilinear forms there refer to the domain of the differential operators, and negative norms enter usually only if Lagrange multipliers are involved. The reader will profit from the modern representation of least-squares methods that does not stop when negative norms or the DeRham complex come into the play. (Zentralblatt) Sujets MSC: 65N30 Numerical analysis -- Partial differential equations, boundary value problems -- Finite elements, Rayleigh-Ritz and Galerkin methods, finite methods
35Q60 Partial differential equations -- Equations of mathematical physics and other areas of application -- PDEs in connection with optics and electromagnetic theory
35K15 Partial differential equations -- Parabolic equations and systems -- Initial value problems for second-order parabolic equations
35L15 Partial differential equations -- Hyperbolic equations and systems -- Initial value problems for second-order hyperbolic equations
65M55 Numerical analysis -- Partial differential equations, initial value and time-dependent initial-boundary value problems -- Multigrid methods; domain decomposition
En-ligne: Springerlink | Zentralblatt | MathSciNet

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... Recent results that are incorporated in the book, refer in particular to negative norm least-squares finite element methods. Note that least-squares formulations refer to the target spaces of the (systems of) differential operators, and minimal regularity leads often to negative norms. In contrast to this fact, the finite element method and the bilinear forms there refer to the domain of the differential operators, and negative norms enter usually only if Lagrange multipliers are involved.
The reader will profit from the modern representation of least-squares methods that does not stop when negative norms or the DeRham complex come into the play. (Zentralblatt)

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