In this book, the author examines mathematical aspects of finite element methods for the approximate solution of incompressible flow problems. The principal goal is to present some of the important mathematical results that are relevant to practical computations. In so doing, useful algorithms are also discussed. Although rigorous results are stated, no detailed proofs are supplied; rather, the intention is to present these results so that they can serve as a guide for the selection and, in certain respects, the implementation of algorithms.
Mathematicians, engineers, and others involved in practical computations.
Discretization of the Primitive Variable Formulation: A Primitive Variable Formulation. The Finite Element Problem and the Div-Stability Condition. Finite Element Spaces. Alternate Weak Forms, Boundary Conditions and Numerical Integration. Penalty Methods. Solution of the Discrete Equations: Newton's Method and Other Iterative Methods. Solving the Linear Systems. Solution Methods for Large Reynolds Numbers. Time Dependent Problems: A Weak Formulation and Spatial Discretizations. Time Discretizations. The Streamfunction-Vorticity Formulation: Algorithms for the Streamfunction-Vorticity Equations. Solution Techniques for Multiply Connected Domains. The Streamfunction Formulation: Algorithms for Determining Streamfunction Approximations. Eigenvalue Problems Connected with Stability Studies for Viscous Flows: Energy Stability Analysis of Viscous Flows. Linearized Stability Analysis of Stationary Viscous Flows. Exterior Problems: Truncated Domain-Artificial Boundary Condition Methods. Nonlinear Constitutive Relations: A Ladyzhenskaya Model and Algebraic Turbulence Models. Bingham Fluids. Electromagnetically or Thermally Coupled Flows: Flows of Liquid Metals. The Boussinesq Equations. Remarks on Some Topics That Have Not Been Considered: Problems, Formulations, Algorithms, and Other Issues That Have Not Been Considered. Bibliography. Glossary of Symbols. Index.
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- © Academic Press 1989
- 28th September 1989
- Academic Press
- eBook ISBN:
- Hardcover ISBN:
@qu:"An excellent guide and can be strongly recommended." @source:--ZENTRALBLATI FUR MATHEMATIK @qu:"Due to the style chosen, the book is easy to read and should also be accessible for engineers who want to know about the variety of rigorous results available...author has succeeded in his goal as formulated in the preface: in writing a book for those who want to get a quick taste of the main points and of the mathematical results available without delving into details." @source:--MATHEMATICAL REVIEWS @qu:"The book is written for the middle ground; the audience that can readily apply the material includes the applied mathematician and the theoretically disposed engineer who seek to use finite element methods for actual flowfield computations." @source:--SIAM REVIEW