Numerical Analysis and Optimization: An Introduction to Mathematical Modelling and Numerical SimulationThis text, based on the author's teaching at École Polytechnique, introduces the reader to the world of mathematical modelling and numerical simulation. Covering the finite difference method; variational formulation of elliptic problems; Sobolev spaces; elliptical problems; the finite element method; Eigenvalue problems; evolution problems; optimality conditions and algorithms and methods of operational research, and including a several exercises throughout, this is an ideal text for advanced undergraduate students and graduates in applied mathematics, engineering, computer science, and the physical sciences. |
Contents
Finite difference method | 31 |
Variational formulation of elliptic problems | 65 |
Sobolev spaces | 79 |
Copyright | |
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Numerical Analysis and Optimization: An Introduction to Mathematical ... Grégoire Allaire Limited preview - 2007 |
Numerical Analysis and Optimization: An Introduction to Mathematical ... Grégoire Allaire Limited preview - 2007 |
Numerical Analysis and Optimization: An Introduction to Mathematical ... Grégoire Allaire No preview available - 2007 |
Common terms and phrases
algorithm apply approximation assume bilinear form boundary value problem bounded set calculate CFL condition class C¹ coefficients constraints continuous linear form convergence convex convex functions deduce defined denote differential equations dimension Dirichlet boundary conditions discrete eigenvalues eigenvectors example Exercise existence and uniqueness explicit scheme finite difference finite element method function gradient graph heat flow equation Hilbert space hypothesis inequality initial data integration iteration L2 norm Laplacian lemma linear system mesh minimization Neumann Neumann boundary conditions nonzero norm numerical obtain open bounded set open set orthogonal P₁ finite element Poincaré inequality polynomial positive definite Proof proposition Remark result satisfies scalar product Section sequence set of RN Show Sobolev space solve stability subspace symmetric theorem un+1 unique solution variational formulation vector verify vertices wave equation zero θη θυ ΘΩ Ω Ω ди дхі