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This book presents some of the latest developments in numerical analysis and scientific computing. Specifically, it covers central schemes, error estimates for discontinuous Galerkin methods, and the use of wavelets in scientific computing.
This volume offers researchers the opportunity to catch up with important developments in the field of numerical analysis and scientific computing and to get in touch with state-of-the-art numerical techniques.
The book has three parts. The first one is devoted to the use of wavelets to derive some new approaches in the numerical solution of PDEs, showing in particular how the possibility of writing equivalent norms for the scale of Besov spaces allows to develop some new methods. The second part provides an overview of the modern finite-volume and finite-difference shock-capturing schemes for systems of conservation and balance laws, with emphasis on providing a unified view of such schemes by identifying the essential aspects of their construction. In the last part a general introduction is given to the discontinuous Galerkin methods for solving some classes of PDEs, discussing cell entropy inequalities, nonlinear stability and error estimates.
This volume offers researchers the opportunity to catch up with important developments in the field of numerical analysis and scientific computing and to get in touch with state-of-the-art numerical techniques.
The book has three parts. The first one is devoted to the use of wavelets to derive some new approaches in the numerical solution of PDEs, showing in particular how the possibility of writing equivalent norms for the scale of Besov spaces allows to develop some new methods. The second part provides an overview of the modern finite-volume and finite-difference shock-capturing schemes for systems of conservation and balance laws, with emphasis on providing a unified view of such schemes by identifying the essential aspects of their construction. In the last part a general introduction is given to the discontinuous Galerkin methods for solving some classes of PDEs, discussing cell entropy inequalities, nonlinear stability and error estimates.
From the reviews:
"It includes an extended version of the lectures given by the four authors at the Advanced School on Numerical Solutions of Partial Differential Equations: New Trends and Applications, held at the CRM - Barcelona between November 15 - 22, 2007. ... The book is addressed to masterands, for PhD candidates and to research workers in the fields of applied mathematics and engineering." (Constantin I. Popovici, IASI Polytechnic Magazine, Vol. 22 (1/4), March-December, 2010)
"The book is well written and organized at a difficulty level that precisely meets the target audiences' needs. ... PhD students as well as engineers and researchers in the field of applied mathematics or scientific computing and interested graduate students will find this book an excellent resource to rapid introduction into the field of modern numerical methods ... . serve as a textbook for graduate - level courses in numerical methods ... . be useful for experienced researchers andpractitioners both from academia or industry." (Andrzej Myslinski, Control and Cybernetics, Vol. 39 (3), 2010)
"It includes an extended version of the lectures given by the four authors at the Advanced School on Numerical Solutions of Partial Differential Equations: New Trends and Applications, held at the CRM - Barcelona between November 15 - 22, 2007. ... The book is addressed to masterands, for PhD candidates and to research workers in the fields of applied mathematics and engineering." (Constantin I. Popovici, IASI Polytechnic Magazine, Vol. 22 (1/4), March-December, 2010)
"The book is well written and organized at a difficulty level that precisely meets the target audiences' needs. ... PhD students as well as engineers and researchers in the field of applied mathematics or scientific computing and interested graduate students will find this book an excellent resource to rapid introduction into the field of modern numerical methods ... . serve as a textbook for graduate - level courses in numerical methods ... . be useful for experienced researchers andpractitioners both from academia or industry." (Andrzej Myslinski, Control and Cybernetics, Vol. 39 (3), 2010)