Finite Elements and Fast Iterative Solvers : with Applications in Incompressible Fluid Dynamics: with Applications in Incompressible Fluid Dynamics
OUP Oxford, May 19, 2005 - Computers - 416 pages
The authors' intended audience is at the level of graduate students and researchers, and we believe that the text offers a valuable contribution to all finite element researchers who would like to broadened both their fundamental and applied knowledge of the field. - Spencer J. Sherwin and Robert M. Kirby, Fluid Mechanics, Vol 557, 2006.
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1 The Poisson equation
2 Solution of discrete Poisson problems
3 The convectiondiffusion equation
4 Solution of discrete convectiondiffusion problems
5 The Stokes equations
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algebraic algorithm analysis associated basis functions bilinear block boundary conditions Chapter coarse grid coefficient matrix Computational Exercise conjugate gradient method constant convection convection–diffusion equation convergence deﬁned derived Dirichlet Dirichlet boundary conditions discussed domain eigenvalues eigenvectors enclosed flow error bound error estimation finite element flow problem Galerkin Gauss–Seidel given gmres ifiss independent of h inf–sup iterative methods Krylov subspace Laplacian Lemma macroelement mass matrix mesh minres mixed approximation multigrid multigrid methods Navier–Stokes equations Newton node nonlinear norm null space operator outflow boundary parameter Peclet number Picard iteration Poisson problem polynomial preconditioner preconditioning pressure convection–diffusion problem in Example Proof Q1 approximation residual Reynolds number satisﬁes satisfy Schur complement Section smoothing solution solver solving space stabilization stabilization matrix Stokes equations Stokes problem strategy streamline diffusion symmetric term Theorem uniform grid vector velocity weak formulation zero