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Mathematical Aspects Of Discontinuous Galerkin Methods

Author: Daniele Antonio Di Pietro
Publisher: Springer Science & Business Media
ISBN: 3642229808
Size: 59.79 MB
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This book introduces the basic ideas to build discontinuous Galerkin methods and, at the same time, incorporates several recent mathematical developments. The presentation is to a large extent self-contained and is intended for graduate students and researchers in numerical analysis. The material covers a wide range of model problems, both steady and unsteady, elaborating from advection-reaction and diffusion problems up to the Navier-Stokes equations and Friedrichs' systems. Both finite element and finite volume viewpoints are exploited to convey the main ideas underlying the design of the approximation. The analysis is presented in a rigorous mathematical setting where discrete counterparts of the key properties of the continuous problem are identified. The framework encompasses fairly general meshes regarding element shapes and hanging nodes. Salient implementation issues are also addressed.

Hp Version Discontinuous Galerkin Methods On Polygonal And Polyhedral Meshes

Author: Andrea Cangiani
Publisher: Springer
ISBN: 3319676733
Size: 60.60 MB
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Over the last few decades discontinuous Galerkin finite element methods (DGFEMs) have been witnessed tremendous interest as a computational framework for the numerical solution of partial differential equations. Their success is due to their extreme versatility in the design of the underlying meshes and local basis functions, while retaining key features of both (classical) finite element and finite volume methods. Somewhat surprisingly, DGFEMs on general tessellations consisting of polygonal (in 2D) or polyhedral (in 3D) element shapes have received little attention within the literature, despite the potential computational advantages. This volume introduces the basic principles of hp-version (i.e., locally varying mesh-size and polynomial order) DGFEMs over meshes consisting of polygonal or polyhedral element shapes, presents their error analysis, and includes an extensive collection of numerical experiments. The extreme flexibility provided by the locally variable elemen t-shapes, element-sizes, and element-orders is shown to deliver substantial computational gains in several practical scenarios.

Building Bridges Connections And Challenges In Modern Approaches To Numerical Partial Differential Equations

Author: Gabriel R. Barrenechea
Publisher: Springer
ISBN: 3319416405
Size: 20.29 MB
Format: PDF
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This volume contains contributed survey papers from the main speakers at the LMS/EPSRC Symposium “Building bridges: connections and challenges in modern approaches to numerical partial differential equations”. This meeting took place in July 8-16, 2014, and its main purpose was to gather specialists in emerging areas of numerical PDEs, and explore the connections between the different approaches. The type of contributions ranges from the theoretical foundations of these new techniques, to the applications of them, to new general frameworks and unified approaches that can cover one, or more than one, of these emerging techniques.

Numerical Mathematics And Advanced Applications Enumath 2013

Author: Assyr Abdulle
Publisher: Springer
ISBN: 3319107054
Size: 38.22 MB
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This book gathers a selection of invited and contributed lectures from the European Conference on Numerical Mathematics and Advanced Applications (ENUMATH) held in Lausanne, Switzerland, August 26-30, 2013. It provides an overview of recent developments in numerical analysis, computational mathematics and applications from leading experts in the field. New results on finite element methods, multiscale methods, numerical linear algebra and discretization techniques for fluid mechanics and optics are presented. As such, the book offers a valuable resource for a wide range of readers looking for a state-of-the-art overview of advanced techniques, algorithms and results in numerical mathematics and scientific computing.

Partial Differential Equations Modeling Analysis And Numerical Approximation

Author: Hervé Le Dret
Publisher: Birkhäuser
ISBN: 3319270672
Size: 40.37 MB
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This book is devoted to the study of partial differential equation problems both from the theoretical and numerical points of view. After presenting modeling aspects, it develops the theoretical analysis of partial differential equation problems for the three main classes of partial differential equations: elliptic, parabolic and hyperbolic. Several numerical approximation methods adapted to each of these examples are analyzed: finite difference, finite element and finite volumes methods, and they are illustrated using numerical simulation results. Although parts of the book are accessible to Bachelor students in mathematics or engineering, it is primarily aimed at Masters students in applied mathematics or computational engineering. The emphasis is on mathematical detail and rigor for the analysis of both continuous and discrete problems.

Theory Numerics And Applications Of Hyperbolic Problems Ii

Author: Christian Klingenberg
Publisher: Springer
ISBN: 3319915487
Size: 57.86 MB
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The second of two volumes, this edited proceedings book features research presented at the XVI International Conference on Hyperbolic Problems held in Aachen, Germany in summer 2016. It focuses on the theoretical, applied, and computational aspects of hyperbolic partial differential equations (systems of hyperbolic conservation laws, wave equations, etc.) and of related mathematical models (PDEs of mixed type, kinetic equations, nonlocal or/and discrete models) found in the field of applied sciences.

Finite Volumes For Complex Applications Iii

Author: Raphaèle Herbin
Publisher: Elsevier Science & Technology
ISBN: 9781903996348
Size: 62.75 MB
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Scientific computing, which involves the analysis of complex systems in real applications with numerical simulations, is becoming an important field of research in itself, in relation to theoretical investigations and physical experiments. In many cases, the underlying mathematical models consist of large systems of partial differential equations, which have to be solved with high accuracy and efficiency. Among the successful methods, in particular for discretizations on unstructured grids, are the Finite Volume schemes. This publication contains the contributions presented at the third Symposium on Finite Volumes for Complex Applications, held in Porquerolles in June 2002. After a critical review of the submitted papers, 96 papers by authors from more than 20 countries are presented in this volume. The subject of these papers ranges from theoretical and numerical results such as theoretical foundation and validation, adaptivity in space and time, higher order discretization and parallelization, to physical applications, such as multiphase flow and flows through porous media, magnetohydrodynamics, reacting and turbulent flows, elastic structures, granular avalanches, and image processing.