<p>This book presents the basic scientific computing methods for the solution of partial differential equations (PDEs) as they occur in engineering problems. Programming codes in Fortran and C are included for each problem. Opening with the definition of the programming environment for the solving of PDE systems, it then addresses in detail the programming of the model problem by the finite element method. Efficiency, compact storage pre-conditioning and mesh adaption are also presented. General elliptic problems and evolution problems are then dealt with. Finally, topics related to other numerical methods, algorithms for parallel computing and multi processor computers are detailed. An integrated software package which illustrates the featured programs of PDEs is available on the Internet via anonymous FTP. The methods presented have applications in numerous fields of engineering including shape optimisation, nuclear safety, heat transfer, acoustics, mechanics of fluids and elasticity, and are also relevant to other areas such as pollution, meteorology, biology, etc.</p>

Introduction to Scientific Computing

Pironneau, Olivier

Lucquin, Brigitte

Computers & Technology

wiley

This volume addresses the methods for solving partial differential equations (PDE) systems. The reader should learn how to write computer programs for the numerical analysis of practical engineering problems. Illustrated by examples, it starts by the definition of a programming environment for the solving of PDE systems by the finite element method. Programming the model problem by a finite element method is then addressed in detail. General elliptic problems and evolution problems are then dealt with. Finally, complements on numerical methods, algorithms for parallel computing and multiprocessor computers are presented.

John Wiley&Sons, Inc.

<p>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.</p>

Partial Differential Equations: Modeling, Analysis and Numerical Approximation (International Series of Numerical Mathematics, 168)

Science & Math

Le Dret, Hervé

Mathematics

Birkhauser

Partial Differential Equations: Modeling, Analysis and Numerical Approximation

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