Buch, Englisch, 556 Seiten, Format (B × H): 152 mm x 229 mm, Gewicht: 795 g
Buch, Englisch, 556 Seiten, Format (B × H): 152 mm x 229 mm, Gewicht: 795 g
ISBN: 978-0-521-56738-1
Verlag: Cambridge University Press
This substantial revision of the text Numerical Solution of Partial Differential Equations by the Finite Element Method by C. Johnson is a two volume introduction to the computational solution of differential equations using a unified approach organised around the adaptive finite element method. It presents a synthesis of mathematical modelling, analysis and computation. It provides the student with theoretical and practical tools useful for addressing the basic questions of computational mathematical modelling in science and engineering: How to model physical phenomena using differential equations? What are the properties of solutions of differential equations? How to compute solutions in practice? How to estimate and control the accuracy of computed solutions? The first volume begins by developing the basic issues at an elementary level in the context of a set of model problems in ordinary differential equations. Covers the basic classes of linear partial differential equations modelling elasticity, heat flow, wave propagation and convection-diffusion-absorption problems. It concludes with a chapter on the abstract framework of the finite element method for differential equations. The second volume extends the scope to nonlinear differential equations and systems of equations modelling a variety of phenomena such as reaction-diffusion, fluid flow and many-body dynamics, and reaches the frontiers of research.
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Part I. Introduction: 1. Introduction; 2. Review of calculus in one dimension; 3. Piecewise polynomial approximation in one dimension; 4. Review of linear algebra; 5. A first example; 6. Review of numerical linear algebra; Part II. Archetypes: 7. An elliptic model problem; 8. A parabolic model problem; 9. A hyperbolic model problem; 10. An elliptic-hyperbolic model problem; 11. Systems of linear ode's; 12. Calculus of variations; 12. Computational mathematical modelling; Part III. Problems in Several Dimensions: 13. Review of calculus in several dimensions; 14. Elliptic problems; 15. The heat equation; 16. The wave equation; 17. Stationary convection-diffusion; 18. Time-dependent convection-diffusion; 19. Eigenvalue problems; 20. Power of abstraction; Part IV. Appendix: 21. History of calculus; 22. Femlab.
