Finite Elements and Fast Iterative Solvers

Howard Elman is a Professor in the Computer Science Department and the Institute for Advanced Computer Studies at the University of Maryland, College Park. He received his doctorate in Computer Science from Yale University in 1982. He has held visiting positions at Stanford University, the University of Manchester Institute of Science and Technology and the University of Oxford. He has served on the editorial boards of SIAM Journal on Scientific Computing, where he was editor-in-chief from 1998-2004, Mathematics of Computation, and Numerical Linear Algebra with Applications. His research concerns numerical solution of partial differential equations, computational fluid dynamics, sparse matrix methods, and uncertainty quantification. David Silvester is a Professor in the School of Mathematics at The University of Manchester. His research concerns numerical solution of partial differential equations, computational fluid dynamics, uncertainty quantification, and high performance computing. He received his doctorate in Mathematics from the University of Manchester Institute of Science and Technology in 1984 and has had visiting positions at Stanford University, the University of Maryland at College Park, and the Université du Littoral, France. He has served on the editorial boards of SIAM Journal on Scientific Computing and the International Journal for Numerical Methods in Fluids. Andy Wathen is Reader in Numerical Analysis at the Oxford University Mathematical Institute, UK and a Fellow at New College. His research focuses on Scientific Computing methods and algorithms associated with the numerical solution of partial differential equations, particularly algorithms of numerical linear algebra. Applications range from coolant flows to biological patterning. He received his doctorate from Reading University in 1982 and has held visiting positions at Stanford University, the University of California, Berkeley and at the University of New South Wales. He has served on the editorial boards of the IMA Journal on Numerical Analysis, SIAM Journal on Scientific Computing, SIAM Journal on Matrix Analysis and Applications, Numerical Linear Algebra with Applications and Electronic Transactions on Numerical Analysis.

0. Models of incompressible fluid flow ; 1. The Poisson equation ; 2. Solution of discrete Poisson problems ; 3. The Stokes equations ; 4. Solution of discrete Stokes problems ; 5. Optimization with PDE constraints ; 6. The convectionDSdiffusion equation ; 7. Solution of discrete convectionDSdiffusion problems ; 8. The NavierDSStokes equations ; 9. Solution of discrete NavierDSStokes problems ; 10. Solution of unsteady NavierDSStokes equations ; 11. Solution of models of buoyancy-driven flow