Stability Estimates for Hybrid Coupled Domain Decomposition Methods

• Κύριος συγγραφέας: Steinbach, Olaf (Συγγραφέας, http://id.loc.gov/vocabulary/relators/aut)
• Συγγραφή απο Οργανισμό/Αρχή: SpringerLink (Online service)
• Μορφή: Ηλεκτρονική πηγή Ηλ. βιβλίο
• Γλώσσα: English
• Έκδοση: Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer, 2003.
• Έκδοση: 1st ed. 2003.
• Σειρά: Lecture Notes in Mathematics, 1809
• Θέματα: Applied mathematics.; Engineering mathematics.; Numerical analysis.; Partial differential equations.; Applications of Mathematics.; Numerical Analysis.; Partial Differential Equations.

Domain decomposition methods are a well established tool for an efficient numerical solution of partial differential equations, in particular for the coupling of different model equations and of different discretization methods. Based on the approximate solution of local boundary value problems eit...

Πίνακας περιεχομένων:

• Preliminaries
• Sobolev Spaces: Saddle Point Problems; Finite Element Spaces; Projection Operators; Quasi Interpolation Operators
• Stability Results: Piecewise Linear Elements; Dual Finite Element Spaces; Higher Order Finite Element Spaces; Biorthogonal Basis Functions
• The Dirichlet-Neumann Map for Elliptic Problems: The Steklov-Poincare Operator; The Newton Potential; Approximation by Finite Element Methods; Approximation by Boundary Element Methods
• Mixed Discretization Schemes: Variational Methods with Approximate Steklov-Poincare Operators; Lagrange Multiplier Methods
• Hybrid Coupled Domain Decomposition Methods: Dirichlet Domain Decomposition Methods; A Two-Level Method; Three-Field Methods; Neumann Domain Decomposition Methods;Numerical Results; Concluding Remarks
• References.