This book is an introduction to the mathematical analysis of p- and hp-finite elements applied to elliptic problems in solid and fluid mechanics. In the last decade the p-, hp-, and spectral element methods have emerged as efficient and robust approximation methods for several classes of problems in this area. The aim of this book is to establish the exponential convergence of such methods for problems with the piecewise analytic solutions which typically arise in engineering. It looks at the variational formulation of boundary value problems with particular emphasis on the regularity of the solution. The books then studies the p- and hp- convergence of the finite element method (FEM) in one and two dimensions, supplying complete proofs. Also covered are hp-FEM for saddle point problems and the techniques for establishing the discrete infsup condition. Finally, hp-FEM in solid mechanics and the issue of locking is addressed in the context of these methods. It is suitable for graduate students and researchers who have had some prior exposure to FEM.
This book is an introduction to the mathematical analysis of p- and hp-finite elements applied to elliptic problems in solid and fluid mechanics. In the last decade the p-, hp-, and spectral element methods have emerged as efficient and robust approximation methods for several classes of problems in this area. The aim of this book is to establish the exponential convergence of such methods for problems with the piecewise analytic solutions which typically arise in engineering. It looks at the variational formulation of boundary value problems with particular emphasis on the regularity of the solution. The books then studies the p- and hp- convergence of the finite element method (FEM) in one and two dimensions, supplying complete proofs. Also covered are hp-FEM for saddle point problems and the techniques for establishing the discrete infsup condition. Finally, hp-FEM in solid mechanics and the issue of locking is addressed in the context of these methods. It is suitable for graduate students and researchers who have had some prior exposure to FEM.
Barnes & Noble is the world’s largest retail bookseller and a leading retailer of content, digital media and educational products. Our Nook Digital business offers a lineup of NOOK® tablets and e-Readers and an expansive collection of digital reading content through the NOOK Store®. Barnes & Noble’s mission is to operate the best omni-channel specialty retail business in America, helping both our customers and booksellers reach their aspirations, while being a credit to the communities we serve.
