@article{as92,
author = "John Atanga and David Silvester",
title = "Iterative methods for stabilized mixed velocity--pressure finite elements",
journal = "Int. J. Numer. Meth. Fluids",
volume = "14",
pages = "71--81",
year = "1992"
}
@article{bps12,
author = "Alexey Bespalov and Catherine Powell and David Silvester",
title = "A priori error analysis of stochastic {G}alerkin mixed approximations
of elliptic {PDE}s with random data",
journal = "SIAM J. Numer. Anal.",
volume = "50",
pages = "2039--2063",
year = "2012",
note = "{\tt http://dx.doi.org/10.1137/110854898}"
}
@article{bps14,
author = "Alexey Bespalov and Catherine Powell and David Silvester",
title = "Energy norm a posteriori error estimation for parametric
operator equations",
journal = "SIAM J. Sci. Comput.",
volume = "36",
pages = "A339--A363",
year = "2014",
note = "{\tt http://dx.doi.org/10.1137/130916849}"
}
@misc{sifiss,
author = "Alex Bespalov and Catherine Powell and David Silvester",
title = "Stochastic {IFISS} ({S-IFISS}) version 1.0",
month ="September",
year = "2013",
note = "available online at {\tt http://www.manchester.ac.uk/ifiss/s-ifiss1.0.tar.gz }"
}
@article{dss13,
author={Sebastien Duminil and Hassane Sadok and David Silvester},
year={2013},
journal={Numerical Algorithms},
doi={10.1007/s11075-013-9726-7},
title={Fast solvers for discretized Navier-Stokes problems using vector extrapolation},
url={{\tt http://dx.doi.org/10.1007/s11075-013-9726-7}},
pages={1-16},
language={English}
}
@article{ehsst07,
author = "Howard Elman and Victoria Howle and John Shadid and David Silvester
and Ray Tuminaro",
title = "Least squares preconditioners for stabilized discretizations
of the {N}avier-{S}tokes equations",
journal = "SIAM J. Sci. Comput.",
volume = "30",
pages = "290--311",
year = "2007"
}
@article{ems11,
author = "Howard Elman and Milan Mihajlovi{\' c} and David Silvester",
title = " Fast iterative solvers for buoyancy driven flow problems",
journal = "J. Comput. Phys.",
volume = "230",
pages = "3900--3914",
year = "2011",
note = "{\tt http://dx.doi.org/10.1016/j.jcp.2011.02.014}"
}
@article{ers07,
author = "Howard Elman and Alison Ramage and David Silvester",
title = "Algorithm {866}: {IFISS}, a {M}atlab toolbox for modelling incompressible flow",
journal = "ACM Trans. Math. Softw.",
volume = "33",
pages = "2--14",
year = "2007"
}
@article{ers14,
author = "Howard Elman and Alison Ramage and David Silvester",
title = "{IFISS}: A computational laboratory for investigating
incompressible flow problem.",
journal = "SIAM Review",
volume = "56",
number = "2",
pages = "261--273",
year = "2014",
note = "{\tt http://dx.doi.org/10.1137/120891393}"
}
@article{es96,
author = "Howard Elman and David Silvester",
title = "Fast nonsymmetric iterations and preconditioning for
{N}avier-{S}tokes equations",
journal = "SIAM J. Sci. Comput.",
volume = "17",
pages = "33--46",
year = "1996"
}
@incollection{esw97,
author = "Howard Elman and David Silvester and Andy Wathen",
title = "Iterative methods for problems in computational fluid dynamics",
editor = "Raymond Chan and Tony Chan and Gene Golub ",
booktitle = "Iterative Methods in Scientific Computing",
publisher = "Springer-Verlag",
address = "Singapore",
pages = "271--327",
year = "1997"
}
@article{esw02,
author = "Howard Elman and David Silvester and Andrew Wathen",
title = "{Performance and analysis of saddle point preconditioners for
the discrete steady-state {N}avier-{S}tokes equations}",
journal = "Numer. Math.",
volume = "90",
pages = "665--688",
year = "2002"
}
@book{esw05,
author = "Howard Elman and David Silvester and Andy Wathen ",
title = "Finite Elements and Fast Iterative Solvers: with Applications
in Incompressible Fluid Dynamics",
publisher = "Oxford University Press",
address = "Oxford",
year = "2005",
note = "xiv+479 pp. ISBN: 978-0-19-852868-5; 0-19-852868-X"
}
@book{esw14,
author = "Howard Elman and David Silvester and Andy Wathen ",
title = "Finite Elements and Fast Iterative Solvers: with Applications
in Incompressible Fluid Dynamics",
publisher = "Oxford University Press",
address = "Oxford, UK",
year = "2014",
note = "Second Edition, xiv+400 pp. ISBN: 978-0-19-967880-8"
}
@article{epsu09,
author = "Oliver Ernst and Catherine Powell and David Silvester and Elisabeth Ullmann",
title = "Efficient solvers for a linear stochastic {G}alerkin mixed formulation
of diffusion problems with random data",
journal = "SIAM J. Sci. Comput.",
volume = "31",
pages = "1424--1447",
year = "2009"
}
@article{frsw98,
author = "Bernd Fischer and Alison Ramage and David Silvester and Andrew Wathen",
title = "Minimum residual methods for augmented systems",
journal = "BIT",
volume = "38",
pages = "527--543",
year = "1998"
}
@article{frsw99,
author = "Bernd Fischer and Alison Ramage and David Silvester and Andrew Wathen",
title = "On parameter choice and iterative convergence for
stabilised discretisations of advection-diffusion problems",
journal = "Comput. Methods Appl. Mech. Engrg.",
volume = "179",
pages = "185--202",
year = "1999"
}
@incollection{gsw96,
author = "Gene Golub and David Silvester and Andrew Wathen",
title = "Diagonal dominance and positive definiteness of upwind
approximations for advection diffusion problems",
editor = "David Griffiths and Alastair G. Watson",
booktitle = " Numerical Analysis: {A.R. Mitchell} {75th} Birthday Volume",
publisher = "World Scientific",
pages = "125--131",
year = "1996"
}
@article{ggs08,
author = "Philip Gresho and David Griffiths and David Silvester",
title = "Adaptive time-stepping for incompressible flow;
part {I}: scalar advection-diffusion",
journal = "SIAM J. Sci. Comput.",
volume = "30",
pages = "2018--2054",
year = "2008"
}
@techreport{gs94,
author = "David Griffiths and David Silvester",
title = "Unstable modes of the {Q1}--{P0} element",
institution = "MIMS",
number = "2011.44",
note = "{\tt http://eprints.ma.man.ac.uk/1628/}",
year = "2011"
}
@article{hsc96,
author = "Richard Hanby and David Silvester and John Chew",
title = "A comparison of coupled and segregated iterative solution
techniques for incompressible swirling flow",
journal = "Int. J. Numer. Meth. Fluids",
volume = "22",
pages = "353--373",
year = "1996"
}
@article{ks99,
author = "David Kay and David Silvester",
title = "A posteriori error estimation for stabilized mixed
approximations of the {S}tokes equations",
journal = "SIAM J. Sci. Comput.",
volume = "21",
pages = "1321--1336",
year = "1999"
}
@article{ks01,
author = "David Kay and David Silvester",
title = "The reliability of local error estimators for
convection-diffusion equations",
journal = "IMA J. Numer. Anal.",
volume = "21",
pages = "107--122",
year = "2001"
}
@article{kggs10,
author = "David Kay and Philip Gresho and David Griffiths and David Silvester",
title = "Adaptive time-stepping for incompressible flow;
part {II}: {N}avier-{S}tokes equations",
journal = "SIAM J. Sci. Comput.",
volume = "32",
pages = " 111--128",
year = "2010"
}
@article{ks92,
author = "Nasserdine Kechkar and David Silvester",
title = "Analysis of locally stabilized mixed finite element
methods for the {S}tokes problem",
journal = "Math. Comput.",
volume = "58",
pages = "1--10",
year = "1992"
}
@article{ls12,
author = "Qifeng Liao and David Silvester",
title = "A simple yet effective a posteriori error estimator for classical mixed approximation
of {S}tokes equations.",
journal = "Appl. Numer. Math.",
volume = "62",
pages = " 1242--1256",
year = "2012",
note = "{\tt http://dx.doi.org/10.1016/j.apnum.2010.05.003}"
}
@article{ls13a,
author = {Liao, Qifeng and Silvester, David},
title = {Robust stabilized Stokes approximation methods for highly stretched grids},
volume = {33},
number = {2},
pages = {413-431},
year = {2013},
note = {{\tt http://dx.doi.org/10.1093/imanum/drs012}},
journal = {IMA Journal of Numerical Analysis}
}
@article{ls13b,
author = "Qifeng Liao and David Silvester",
title = "Implicit solvers using stabilized mixed approximation",
journal = "Int. J. Numer. Meth. Fluids",
volume = "33",
pages = "413--431",
year = "2013",
note = "http://dx.doi.org/10.1002/fld.3697"
}
@article{ms04,
author = "Milan Mihajlovi{\' c} and David Silvester",
title = "Efficient parallel solvers for the biharmonic equation,",
journal = "Parallel Computing",
volume = "30",
pages = "35--55",
year = "2004"
}
@article{ns98,
author = "Sean Norburn and David Silvester",
title = "Stable vs. stabilised mixed methods for incompressible flow",
journal = "Comput. Methods Appl. Mech. Engrg",
volume = "166",
pages = "131--141",
year = "1998"
}
@article{ns01,
author = "Sean Norburn and David Silvester",
title = " Fourier analysis of stabilised ${Q}_1$--${Q}_1$ mixed finite element approximation",
journal = "SIAM J. Numer. Anal.",
volume = "39",
pages = "817--833",
year = "2001"
}
@incollection{ps02,
author = "Catherine Powell and David Silvester",
title = "Black-box preconditioning for mixed formulation of self-adjoint elliptic {PDEs}",
editor = "Eberhard B{\" a}nsch",
booktitle = "Challenges in Scientific Computing---CISC 2002",
publisher = "Springer Lecture Notes in Computational Science and Engineering",
address = "Berlin",
volume = "35",
pages = "268--285",
year = "2003"
}
@article{ps04,
author = "Catherine Powell and David Silvester",
title = "Optimal preconditioning for {R}aviart-{T}homas mixed formulation of
second-order elliptic problems",
journal = "SIAM J. Matrix Anal. Appl.",
volume = "25",
pages = " 718--738",
year = "2004"
}
@article{ps12,
author = "Catherine Powell and David Silvester",
title = "Preconditioning steady-state {N}avier--{S}tokes equations with random data",
journal = "SIAM J. Sci. Comput.",
volume = "34",
pages = "A2482--A2506",
year = "2012",
note = "{\tt http://dx.doi.org/10.1137/120870578}"
}
@article{s88,
author = "David Silvester",
title = " Optimising finite element matrix calculations using the general technique of
element vectorisation",
journal = "Parallel Computing",
volume = "6",
pages = "157--164",
year = "1988"
}
@article{s94,
author = "David Silvester",
title = "Optimal low order finite element methods for incompressible flow",
journal = "Comput. Methods Appl. Mech. Engrg",
volume = "111",
pages = "357--368",
year = "1994"
}
@Incollection{s13,
author = {David Silvester},
booktitle = {Encyclopedia of Applied and Computational Mathematics},
title = {Preconditioning},
note = {ISBN 978-3-540-70529-1}
publisher = {Springer-Verlag Berlin Heidelberg},
year = {2016}
}
@article{sbp12,
author = "David Silvester and Alexey Bespalov and Catherine Powell",
title = "A framework for the development of implicit solvers for incompressible flow problems",
journal = "Discrete and Continuous Dynamical Systems---Series S",
volume = "5",
pages = "1195--1221",
year = "2012",
note = "{\tt http://dx.doi.org/10.3934/dcdss.2012.5.1195}"
}
@misc{primer,
author = "David Silvester",
title = "A {F}inite {E}lement {P}rimer: version 1.1",
note = "available online at {\tt http://www.maths.manchester.ac.uk/djs/primer.pdf}",
year = "2009"
}
@article{sekw01,
author = "David Silvester and Howard Elman and David Kay and Andrew Wathen",
title = "Efficient preconditioning of the linearised {N}avier-{S}tokes equations
for incompressible flow",
journal = "J. Comp. Appl. Math.",
volume = "128",
pages = "261--279",
year = "2001"
}
@misc{ifiss,
author = "David Silvester and Howard Elman and Alison Ramage",
title = "{I}ncompressible {F}low and {I}terative {S}olver {S}oftware ({IFISS}), version 3.3",
month = "October",
year = "2013",
note = "{\tt http://www.manchester.ac.uk/ifiss/}" }
@article{sk90,
author = "David Silvester and Nasserdine Kechkar",
title = "Stabilised bilinear--constant velocity--pressure finite elements for the conjugate gradient
solution of the {S}tokes problem",
journal = "Comput. Methods Appl. Mech. Engrg",
volume = "79",
pages = "71--86",
year = "1990"
}
@article{sm04,
author = "David Silvester and Milan Mihajlovi{\' c}",
title = "A black-box multigrid preconditioner for the biharmonic equation",
journal = "BIT",
volume = "44",
pages = "151--163",
year = "2004"
}
@misc{pifiss,
author = "David Silvester and Catherine Powell",
title = " {P}otential {I}ncompressible {F}low and {I}terative {S}olver {S}oftware ({PIFISS})",
month ="February",
year = "2007",
note = "available online at {\tt http://www.manchester.ac.uk/ifiss/pifiss}"
}
@techreport{pifiss-guide,
author = "David Silvester and Catherine Powell",
title = "{P}otential ({I}ncompressible) {F}low and {I}terative {S}olution
{S}oftware {G}uide ({PIFISS}) version 1.0",
institution = "MIMS",
number = "2007.14",
note = "{\tt http://eprints.ma.man.ac.uk/700/}",
year = "2007"
}
@article{ss97,
author = "Anthony Smith and David Silvester",
title = "Implicit algorithms and their linearisation for the transient {N}avier-{S}tokes equations",
journal = "IMA J. Numer. Anal.",
volume = "17",
pages = "527--545",
year = "1997"
}
@article{ss03,
author = "Syamsudhuha and David Silvester",
title = "{Efficient solution of the steady-state {N}avier-{S}tokes
equations using a multigrid preconditioned {N}ewton-{K}rylov method}",
journal = "Int. J. Numer. Methods Fluids",
volume = "43",
pages = "1407--1427",
year = "2003"
}
@article{ss11,
author = "David Silvester and Valeria Simoncini",
title = "An optimal iterative solver for symmetric indefinite
systems stemming from mixed approximation",
journal = "ACM Trans. Math. Softw.",
volume = " 37",
number = "4",
year = "2011",
note = " http://dx.doi.org/10.1145/1916461.1916466"
}
@article{ssm13,
author = "Chris Smethurst and David Silvester and Milan Mihajlovi{\' c}",
title = "Unstructured finite element method for the solution of the
Boussinesq problem in three dimensions",
journal = "Int. J. Numer. Methods Fluids",
note = "http://dx.doi.org/10.1002/fld.3823"
}
@article{st86,
author = "David Silvester and Ron Thatcher",
title = "The effect of the stability of mixed finite element approximations on the accuracy
and rate of convergence of solution when solving incompressible flow problems",
journal = "Int. J. Numer. Methods Fluids",
volume = "6",
pages = "841--853",
year = "1986"
}
@article{std84,
author = "David Silvester and Ron Thatcher and John Duthie",
title = "The specification and numerical solution of a benchmark swirling laminar flow problem",
journal = "Comput. Fluids",
volume = "12",
pages = " 281--292",
year = "1984"
}
@article{sw94,
author = "David Silvester and Andrew Wathen",
title = "Fast iterative solution of stabilised {S}tokes
systems. {P}art {II}: Using general block preconditioners",
journal = "SIAM J. Numer. Anal.",
volume = "31",
pages = "1352--1367",
year = "1994"
}
@incollection{sw96,
author = "David Silvester and Andrew Wathen",
title = "Fast \& robust solvers for time-discretised incompressible {N}avier-{S}tokes equations",
editor = "David Griffiths and Alastair G. Watson",
booktitle = "Numerical Analysis 1995",
publisher = "Longman Scientific",
pages = "154--168",
year = "1996"
}
@article{ws93,
author = "Andrew Wathen and David Silvester",
title = "Fast iterative solution of stabilised {S}tokes
systems. {P}art {I}: Using simple diagonal preconditioners",
journal = "SIAM J. Numer. Anal.",
volume = "30",
pages = "630--649",
year = "1993"
}
@article{wfs95,
author = "Andrew Wathen and Bernd Fischer and David Silvester",
title = "The convergence rate of the minimal residual method for the {S}tokes problem,",
journal = "Numer. Math.",
volume = "71",
pages = "121--134",
year = "1995"
}
@incollection{wfs98,
author = "Andrew Wathen and Bernd Fischer and David Silvester",
title = "The convergence of iterative solution methods for symmetric and
indefinite systems",
editor = "David Griffiths and Desmond Higham and Alastair G. Watson",
booktitle = "Numerical Analysis 1997",
publisher = "Longman Scientific",
pages = "230--240",
year = "1998"
}
@misc{hsl,
title = " The {HSL} {M}athematical {S}oftware {L}ibrary",
note = " {\tt http://www.hsl.rl.ac.uk/}",
year = "2013"
}
@article{hslcode,
author = "Jonathan Boyle and Milan Mihajlovi\'{c} and Jennifer Scott",
title = "{HSL\_MI20}: an efficient {AMG} preconditioner for
finite element problems in {3D}",
journal = "Int. J. Numer. Meth. Engng.",
volume = "82",
pages = "64--98",
year = "2010"
}
@misc{rpdes,
title = "Analysis of {N}umerical {M}ethods for {PDE}s with {R}andom {D}ata",
note = "{\tt http://www.maths.manchester.ac.uk/djs/rpdes.html}",
year = "2014"
}