Least-squares finite element methods / Pavel B. Bochev, Max D. Gunzburger
Type de document : Livre numériqueCollection : Applied mathematical sciences, 166Langue : anglais.Éditeur : New York : Springer, 2009ISBN: 9780387308883.ISSN: 0066-5452.Sujet MSC : 65N30, Numerical methods for PDEs, boundary value problems, Finite element, Rayleigh-Ritz and Galerkin methods35Q60, PDEs of mathematical physics and other areas of application, PDEs in connection with optics and electromagnetic theory
35K15, PDEs - Parabolic equations and parabolic systems, Initial value problems for second-order parabolic equations
35L15, PDEs - Hyperbolic equations and hyperbolic systems, Initial value problems for second-order hyperbolic equations
65M55, Numerical analysis, Multigrid methods; domain decomposition for initial value and initial-boundary value problems involving PDEsEn-ligne : Springerlink | Zentralblatt | MathSciNet
... 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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