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This book discusses a family of computational methods, known as discontinuous Galerkin methods, for solving partial differential equations. While these methods have been known since the early 1970s, they have experienced an almost explosive growth interest during the last ten to fifteen years, leading both to substantial theoretical developments and the application of these methods to a broad range of problems. These methods are different in nature from standard methods such as finite element or finite difference methods, often presenting a challenge in the transition from theoretical developments to actual implementations and applications. This book is aimed at graduate level classes in applied and computational mathematics. The combination of an in depth discussion of the fundamental properties of the discontinuous Galerkin computational methods with the availability of extensive software allows students to gain first hand experience from the beginning without eliminating theoretical insight. Jan S. Hesthaven is a professor of Applied Mathematics at Brown University. Tim Warburton is an assistant professor of Applied and Computational Mathematics at Rice University.

Galerkin methods. --- Finite element method. --- Differential equations, Partial. --- Numerical analysis. --- Engineering. --- Mathematical physics. --- Differential equations, partial. --- Numerical Analysis. --- Computational Intelligence. --- Mathematical Methods in Physics. --- Partial Differential Equations. --- Partial differential equations --- Physical mathematics --- Physics --- Construction --- Industrial arts --- Technology --- Mathematical analysis --- Mathematics --- Computational intelligence. --- Physics. --- Partial differential equations. --- Natural philosophy --- Philosophy, Natural --- Physical sciences --- Dynamics --- Intelligence, Computational --- Artificial intelligence --- Soft computing

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This book provides a thorough introduction to the mathematical and algorithmic aspects of certified reduced basis methods for parametrized partial differential equations. Central aspects ranging from model construction, error estimation and computational efficiency to empirical interpolation methods are discussed in detail for coercive problems. More advanced aspects associated with time-dependent problems, non-compliant and non-coercive problems and applications with geometric variation are also discussed as examples.

Mathematics - General --- Mathematics --- Physical Sciences & Mathematics --- Differential equations, Partial. --- Partial differential equations --- Computer science --- Differential equations, partial. --- Engineering mathematics. --- Mathematics. --- Computational Mathematics and Numerical Analysis. --- Partial Differential Equations. --- Mathematical and Computational Engineering. --- Theoretical, Mathematical and Computational Physics. --- Applications of Mathematics. --- Math --- Science --- Engineering --- Engineering analysis --- Mathematical analysis --- Computer mathematics --- Discrete mathematics --- Electronic data processing --- Computer mathematics. --- Partial differential equations. --- Applied mathematics. --- Mathematical physics. --- Physical mathematics --- Physics

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This book provides a thorough introduction to the mathematical and algorithmic aspects of certified reduced basis methods for parametrized partial differential equations. Central aspects ranging from model construction, error estimation and computational efficiency to empirical interpolation methods are discussed in detail for coercive problems. More advanced aspects associated with time-dependent problems, non-compliant and non-coercive problems and applications with geometric variation are also discussed as examples.

Partial differential equations --- Mathematics --- Mathematical physics --- Physics --- Applied physical engineering --- Engineering sciences. Technology --- Computer. Automation --- differentiaalvergelijkingen --- analyse (wiskunde) --- toegepaste wiskunde --- theoretische fysica --- computers --- economie --- informatica --- wiskunde --- ingenieurswetenschappen --- fysica

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The book contains a selection of high quality papers, chosen among the best presentations during the International Conference on Spectral and High-Order Methods (2014), and provides an overview of the depth and breadth of the activities within this important research area.  The carefully reviewed selection of papers will provide the reader with a snapshot of the state-of-the-art and help initiate new research directions through the extensive biography.

Mathematics - General --- Mathematics --- Physical Sciences & Mathematics --- Differential equations, Partial --- Spectral theory (Mathematics) --- Conferences - Meetings --- Numerical solutions --- Mathematics. --- Computer science --- Partial differential equations. --- Applied mathematics. --- Engineering mathematics. --- Computer mathematics. --- Numerical analysis. --- Computational Science and Engineering. --- Numerical Analysis. --- Partial Differential Equations. --- Applications of Mathematics. --- Mathematics of Computing. --- Mathematical analysis --- Computer mathematics --- Discrete mathematics --- Electronic data processing --- Engineering --- Engineering analysis --- Partial differential equations --- Math --- Science --- Computer science. --- Differential equations, partial. --- Informatics --- Computer science—Mathematics.

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This book discusses a family of computational methods, known as discontinuous Galerkin methods, for solving partial differential equations. While these methods have been known since the early 1970s, they have experienced an almost explosive growth interest during the last ten to fifteen years, leading both to substantial theoretical developments and the application of these methods to a broad range of problems. These methods are different in nature from standard methods such as finite element or finite difference methods, often presenting a challenge in the transition from theoretical developments to actual implementations and applications. This book is aimed at graduate level classes in applied and computational mathematics. The combination of an in depth discussion of the fundamental properties of the discontinuous Galerkin computational methods with the availability of extensive software allows students to gain first hand experience from the beginning without eliminating theoretical insight. Jan S. Hesthaven is a professor of Applied Mathematics at Brown University. Tim Warburton is an assistant professor of Applied and Computational Mathematics at Rice University.

Numerical analysis --- Computer. Automation --- algoritmen --- Mathematical physics --- numerieke analyse --- differentiaalvergelijkingen --- wiskunde --- Partial differential equations --- fysica --- Differential equations, Partial --- Finite element method --- Galerkin methods --- 519.63 --- 681.3 *G18 --- Sinc-Galerkin methods --- Sinc methods --- FEA (Numerical analysis) --- FEM (Numerical analysis) --- Finite element analysis --- Isogeometric analysis --- 519.63 Numerical methods for solution of partial differential equations --- Numerical methods for solution of partial differential equations --- 681.3 *G18 Partial differential equations: difference methods; elliptic equations; finite element methods; hyperbolic equations; method of lines; parabolic equations (Numerical analysis) --- Partial differential equations: difference methods; elliptic equations; finite element methods; hyperbolic equations; method of lines; parabolic equations (Numerical analysis)