Table Of Content108
Petr Knobloch Editor
Boundary and Interior
Layers, Computational
and Asymptotic
Methods – BAIL 2014
Editorial Board
T. J.Barth
M.Griebel
D.E.Keyes
R.M.Nieminen
D.Roose
T.Schlick
Lecture Notes
in Computational Science 108
and Engineering
Editors:
TimothyJ.Barth
MichaelGriebel
DavidE.Keyes
RistoM.Nieminen
DirkRoose
TamarSchlick
Moreinformationaboutthisseriesathttp://www.springer.com/series/3527
Petr Knobloch
Editor
Boundary and Interior
Layers, Computational
and Asymptotic
Methods – BAIL 2014
123
Editor
PetrKnobloch
FacultyofMathematicsandPhysics
CharlesUniversityinPrague
Praha,CzechRepublic
ISSN1439-7358 ISSN2197-7100 (electronic)
LectureNotesinComputationalScienceandEngineering
ISBN978-3-319-25725-9 ISBN978-3-319-25727-3 (eBook)
DOI10.1007/978-3-319-25727-3
LibraryofCongressControlNumber:2015957960
MathematicsSubjectClassification(2010):34-XX,35-XX,65Lxx,65Mxx,65Nxx,76Dxx.
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Preface
These Proceedings contain contributions reflecting a selection of the lectures
presented at the conference BAIL 2014: Boundary and Interior Layers – Compu-
tationaland Asymptotic Methods, which was held from 15 to 19 September 2014
at Charles University in Prague, Czech Republic. Apart from two hiatuses, the
BAIL conferences have been held every 2 years and BAIL 2014 was already the
14th conference in this series. The first three BAIL conferences were organized
by Professor John Miller in Dublin (1980, 1982, 1984). The next ten were held
in Novosibirsk (1986), Shanghai (1988), Colorado (1992), Beijing (1994), Perth
(2002),Toulouse(2004),Göttingen(2006),Limerick(2008),Zaragoza(2010),and
Pohang(2012).BAIL2016isplannedforBeijing.
The conference BAIL 2014 attracted 54 participants from 15 countries in
three continents. They presented 50 lectures, five of which were invited. Almost
half of the speakers present the contents of their lectures in these Proceedings.
The conference included two mini-symposia devoted to stabilized methods in
aerodynamics modeling and tailored finite point method for problems with non-
smooth solution. As usual, both mathematicians(pure and applied) and engineers
participatedinthisBAILconference,whichledtoaveryfruitfulexchangeofideas.
A positive aspectwas also the participationof severalPhD students, showingthat
thetopicsoftheconferenceremainattractivealsoforyoungscientists.Thelectures
at the conferencecomprisedboth rigorousmathematicalresults on problemswith
layers and their numericalsolution and complicated computationaltechniquesfor
advancedapplications.
ThecontributionsintheseProceedingsaredevotedtotheoreticaland/ornumer-
ical analysis of problems involving boundary and interior layers and of methods
forsolvingtheseproblemsnumerically.Almosthalfofthecontributionsstudyfluid
flowproblems,whereastheremainingcontributionscontainresultsonconvection–
diffusion, convection–diffusion–reaction, and reaction–diffusion equations. Both
steadyandtransientproblemsareconsidered.Mostofthenumericalschemespre-
sentedintheseProceedingsarebasedonthefiniteelementmethod,closelyfollowed
by the finite difference method. Nevertheless, in three cases, also solvers based
on the finite volume method are applied. The topics covered by the contributions
v
vi Preface
include theoretical analyses of various (stabilized) numerical schemes, typically
represented by stability results and error estimates; analyses for various adapted
meshes,inparticular,uniformerrorestimatesonShishkinmeshes;aposteriorierror
estimation; various approaches to turbulence modelling; studies of the influence
offiniteprecisionarithmetic;computationaltechniquesforadvancedapplications;
asymptotic theory of boundary layers; and investigations of layer phenomena in
convection–diffusionproblemswithfractionalderivatives.Almostallcontributions
contain numerical results illustrating the respective theoretical considerations. In
view of the wide variety of topics treated in the contributions, the Proceedings
provide a very good overview of current research into the theory and numerical
solutionofproblemsinvolvingboundaryandinteriorlayers.
All contributions in the Proceedings were subject to a standard refereeing
process.Iwouldliketothanktheauthorsofthecontributionsfortheircooperation
andtheunnamedrefereesfortheirvaluablesuggestionsthatcontributedtothehigh
qualityofthisvolume.
I also wish to thank the organizers of the mini-symposia at BAIL 2014, all
the attendees for their active participation in the conference, and my colleagues
Hana Orosová, Jiˇrí Felcman, Jan Lamacˇ, and Petr Lukáš for their help with the
organizationoftheconference.
Praha,CzechRepublic PetrKnobloch
August2015
Contents
ANoteontheStabilisedQ1(cid:2)P0 MethodonQuadrilaterals
withHighAspectRatios......................................................... 1
GabrielR.BarrenecheaandAndreasWachtel
APosterioriErrorEstimationofaStabilizedMixedFinite
ElementMethodforDarcyFlow............................................... 13
TomásPatricioBarrios,JoséManuelCascón,andMaríaGonzález
A LocalProjectionStabilizedLagrange-GalerkinMethod
forConvection-DiffusionEquations............................................ 25
RodolfoBermejo,RafaelCantón,andLauraSaavedra
Outflow Conditions for the Navier-Stokes Equations
withSkew-SymmetricFormulationoftheConvectiveTerm................ 35
MalteBraack
Finite Element Approximation of an Unsteady
Projection-Based VMS Turbulence Model with Wall
Laws ............................................................................... 47
Tomás Chacón Rebollo, Macarena Gómez Mármol,
andSamueleRubino
Spatial Semidiscretizations and Time Integrationof 2D
ParabolicSingularlyPerturbedProblems .................................... 75
CarmeloClaveroandJuanCarlosJorge
BoundaryLayersinaRiemann-LiouvilleFractionalDerivative
Two-PointBoundaryValueProblem........................................... 87
JoséLuisGraciaandMartinStynes
OntheApplicationofAlgebraicFlux CorrectionSchemes
toProblemswithNon-vanishingRight-HandSide........................... 99
PetrKnobloch
vii
viii Contents
InvestigationofNumericalWallFunctionsBasedonthe1D
Boundary-LayerEquationsforFlowswithSignificantPressure
Gradient........................................................................... 111
TobiasKnopp,FabianSpallek,OctavianFrederich,andGerdRapin
ModifiedSUPGMethodonOrientedMeshes ................................ 121
JanLamacˇ
On Numerical Simulation of Transition to Turbulence
inTurbineCascade............................................................... 135
PetrLouda,KarelKozel,andJaromírPˇríhoda
UnderstandingtheLimitsofInf-SupStableGalerkin-FEM
forIncompressibleFlows........................................................ 147
GertLube,DanielArndt,andHeleneDallmann
APosterioriOptimizationofParametersintheSUPGMethod
forHigherDegreeFESpaces................................................... 171
PetrLukáš
A Parameter-UniformFirstOrderConvergentNumerical
MethodforaSystemofSingularlyPerturbedSecondOrder
DelayDifferentialEquations.................................................... 183
ManikandanMariappan,JohnJ.H.Miller,andValarmathiSigamani
NumericalSimulationofAirJetAttachmenttoConvexWalls
andApplicationtoUAV ......................................................... 197
NikolaMirkovandBoškoRašuo
CholeskyFactorisationofLinearSystemsComingfromFinite
DifferenceApproximationsofSingularlyPerturbedProblems............. 209
TháiAnhNhanandNiallMadden
NumericalExperimentswithaLinearConvection–Diffusion
ProblemContainingaTime-VaryingInteriorLayer ........................ 221
EugeneO’RiordanandJasonQuinn
Second Order Uniformly Convergent Numerical
Method for a Coupled System of Singularly Perturbed
Reaction-DiffusionProblemswithDiscontinuousSourceTerm............ 233
S.ChandraSekharaRaoandSheetalChawla
AMultiscaleSparseGridTechnique foraTwo-Dimensional
Convection-DiffusionProblemwithExponentialLayers.................... 245
StephenRussellandNiallMadden
OntheDelayandInviscidNatureofTurbulent Break-Away
SeparationintheHigh-ReLimit ............................................... 257
BernhardScheichl
Contents ix
UseofStandardDifferenceSchemeonUniformGrids
forSolvingSingularlyPerturbedProblemsUnderComputer
Perturbations..................................................................... 269
GrigoriiShishkin
DifferenceSchemesofHighAccuracyOrderonUniformGrids
foraSingularlyPerturbedParabolicReaction-DiffusionEquation ....... 281
LidiaShishkina
Blow-Up of Solutions and Interior Layers in a Caputo
Two-PointBoundaryValueProblem........................................... 293
MartinStynesandJoséLuisGracia
On Finite Element Approximation of Fluid-Structure
InteractionswithConsiderationofTransitionModel........................ 303
PetrSvácˇek
