Advances in the Finite Element Method for Fluid Flow: Stabilized Methods, A-Posteriori Error Estimation and Mesh Adaptivity

Hamdy Doweidar, Mohamed

ISBN 10: 3639369939 / ISBN 13: 9783639369939

Published by VDM Verlag Dr. Müller, 2011

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Bibliographic Details

• Title: Advances in the Finite Element Method for Fluid Flow: Stabilized Methods, A-Posteriori Error Estimation and Mesh Adaptivity
• Publisher: VDM Verlag Dr. Müller
• Publication Date: 2011
• Language: English
• ISBN 10: 3639369939
• ISBN 13: 9783639369939
• Binding: Paperback
• Condition: Like New
• Book Type: book

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Synopsis

Throughout this book three main topics are presented. The first one presents the new SGS/GSGS variational formulation. The local stability of this method is much better than that of the present stabilized methods. Moreover, in the advective-diffusive limit and for piecewise linear functional spaces, the method recovers the classical SUPG method. The second topic is the analysis of the most common transient methods for the transient advection-diffusion-reaction equation. This analysis includes semi-discrete, time-discontinuous space-time stabilized finite element methods and several predictor multi-corrector versions. In the last topic, a new explicit a-posteriori error estimator is presented, which is derived from the variational multiscale theory. The error estimator uses an approximation of the Green's function, which reproduces the error according to the dual problem. The technique is applied to fluid flow transport, showing that for convection-dominated flows, the efficiency index is independent of the diffusion coefficient.

About the Author

Dr. Doweidar is associate professor at the Mechanical Eng. Dpt., Uni. of Zaragoza, Spain. He is a member of the Group of Structural Mechanics and Materials Modelling (GEMM); Biomedical Research Networking center in Bioengineering, Biomaterials and Nanomedicine (CIBER-BBN) and Aragón Institute of Eng. Research (I3A). (e-mail: mohamed@unizar.es)