Finite Elements and Fast Iterative Solvers: with Applications in Incompressible Fluid Dynamics

By Howard C. Elman, D. Silvester, A. Wathen. 2014

1,040 citations recorded by the source corpus.

Subfields: Computational Mechanics, Computational Theory and Mathematics

View Paper: https://www.semanticscholar.org/paper/8551c0ad0e4e9b4d98aa7a7d92cecb433be3c3e3

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In Computational Mechanics

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Citations in the corpus

Algorithm 866: IFISS, a Matlab toolbox for modelling incompressible flow (2007, methodology): “Further details can be found in the user manual accompanying the software [Elman et al. 2005a], along with a description of how the model problems can be easily adapted to deal with new domains, PDE features or boundary conditions.”
BOUNDARY CONDITIONS IN APPROXIMATE COMMUTATOR PRECONDITIONERS FOR THE NAVIER-STOKES EQUATIONS ∗ (2009, positive): “This is fundamentally different from what has been done previously [5], where either a Neumann or Dirichlet condition is imposed on a boundary depending on whether it corresponds to inflow, outflow, or no slip.”
Automated Solution of Differential Equations by the Finite Element Method: The FEniCS Book (2012, background): “Preconditioners of this form has been studied by many; see for example Cahouet and Chabard (1988); Elman et al. (2005); Mardal and Winther (2004, 2011); Turek (1999).”
Recent computational developments in Krylov subspace methods for linear systems (2007, background): “This can be appreciated by a cursory look at any journal in science or engineering; see also the very recent book [100].”
Low-rank solvers for unsteady Stokes–Brinkman optimal control problem with random data (2016, neutral): “Fortunately, though, BM−1BT 4 is spectrally equivalent to the Laplacian Kp defined on the pressure space [13]; that is, Kp ∼ BM−1BT in 5 the sense that there exist constants c0 and c1 independent of h such that 0 < c0 ≤ c1 <∞ with 6”
Neurobiology of Aging: Contents (2005, neutral): “For detailed discussions of the use of multigrid components in the solution of saddle point problems from finite element discretizations, the reader is referred to Elman et al. (2005c) and Turek (1999); see also the recent survey by Wesseling and Oosterlee (2001).”
Numerical Methods for Evolutionary Differential Equations (2008, methodology): “Many textbooks have been written on this subject, including [158, 104, 67, 73, 35, 59].”