Multilevel Finite Element Approximation

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Beschreibung

These notes reflect, to a great part, the present research interests of the author but were influenced by the ideas and the work of many colleagues. They are based on lectures given by the author at the Institutes of Mathematics and Informatics at the Technical U niversity of Munich during February /March 1993. I wish to warmly thank ehr. Zenger and R. Hoppe for their generous support and the many discussions I had with them and their younger colleagues during the last year. Part of the results contained in section 4 is the output of these discussions and joint work with M. Griebel. There are many other mathematicians who encouraged me (or personally or by their mathematical work) to step into the field of multilevel methods. I want to acknowledge the support I received from W. Dahmen, R. A. DeVore, P. Deufl hard, W. Hackbusch, H. Trieb el , O. Widlund, H. Yserentant and many others. On the other hand, I should apologize for not mentioning many interesting re search results and names standing for recent developments in the fields which are the subject of these notes. Finally, I want to thank my family, my wife Olga and my daughters Evelyn and Annelie, for their everyday patience and support.

Inhaltsverzeichnis

1 Introduction.- 2 Finite element approximation.- 2.1 Finite elements, multivariate splines, wavelets.- 2.2 Moduli of smoothness and K-functionals.- 2.3 Jackson and Whitney inequalities.- 2.4 Bernstein inequalities and inverse estimates.- 2.5 Information on other approximation schemes.- 2.6 Constructive characterization of Besov spaces.- 3 Function spaces.- 3.1 Spaces on Rd.- 3.2 Spaces on domains and extension.- 3.3 Spaces on manifolds and traces.- 3.4 Approximation spaces on polyhedral domains.- 4 Applications to multilevel methods.- 4.1 The abstract Schwarz theory.- 4.2 Second-order elliptic equations.- 4.3 The biharmonic problem.- 4.4 Domain decomposition and boundary element methods.- 4.5 Sparse grids.- 4.6 Nonconforming and mixed methods.- 5 Error estimates and adaptivity.- 5.1 Traditional error estimates.- 5.2 h-version and nonlinear approximation.- 5.3 Adaptive multilevel methods.- 5.4 More complicated approximation schemes.- References.

Details

Erscheinungsjahr:	1994
Fachbereich:	Allgemeines
Genre:	Mathematik , Medizin , Naturwissenschaften , Technik
Rubrik:	Naturwissenschaften & Technik
Medium:	Taschenbuch
Inhalt:	160 S.
ISBN-13:	9783519027195
ISBN-10:	3519027194
Sprache:	Deutsch
Einband:	Kartoniert / Broschiert
Autor:	Oswald, Peter
Hersteller:	Vieweg & Teubner Vieweg+Teubner Verlag
Verantwortliche Person für die EU:	Springer Vieweg in Springer Science + Business Media, Abraham-Lincoln-Str. 46, D-65189 Wiesbaden, juergen.hartmann@springer.com
Maße:	244 x 170 x 10 mm
Von/Mit:	Peter Oswald
Erscheinungsdatum:	01.01.1994
Gewicht:	0,296 kg