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2.1 Model Problem 7 -- 2.2 Mesh-based Elements 9 -- 2.3 Sobolev Spaces 12 -- 2.4 Abstract Variational Problems 16 -- 2.5 Approximation Error 19 -- 3 B-splines 23 -- 3.2 Definition And Basic Properties 25 -- 3.3 Recurrence Relation 27 -- 3.4 Representation Of Polynomials 29 -- 3.5 Subdivision 32 -- 3.6 Scalar Products 35 -- 4 Finite Element Bases 37 -- 4.1 Multivariate B-splines 37 -- 4.2 Splines On Bounded Domains 40 -- 4.3 Weight Functions 43 -- 4.4 Web-splines 46 -- 4.5 Hierarchical Bases 50 -- 5 Approximation With Weighted Splines 53 -- 5.1 Dual Functions 53 -- 5.2 Stability 56 -- 5.3 Polynomial Approximation 60 -- 5.4 Quasi-interpolation 63 -- 5.5 Boundary Regularity 65 -- 5.6 Error Estimates For Standard Weight Functions 67 -- 6 Boundary Value Problems 71 -- 6.1 Essential Boundary Conditions 71 -- 6.2 Natural Boundary Conditions 75 -- 6.3 Mixed Problems With Variable Coefficients 79 -- 6.4 Biharmonic Equation 82 -- 6.5 Linear Elasticity 86 -- 6.6 Plane Strain And Plane Stress 89 -- 7 Multigrid Methods 95 -- 7.1 Multigrid Idea Klaus Höllig. Includes Bibliographical References (p. 137-142) And Index.

Author

Höllig, Klaus

Publisher

Society for Industrial and Applied Mathematics (SIAM, 3600 Market Street, Floor 6, Philadelphia, PA 19104)

Published

2003

Language

EN

ISBN

9781613446676

Subjects

Engineering, Mathematics, Technology