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On the Adaptive Finite Element Solution of Partial Differential Equations Using h-r-Refinem

On the Adaptive Finite Element Solution of Partial Differential Equations Using h-r-Refinem

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时间：2019-05-27

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1、UniversityofLeedsSCHOOLOFCOMPUTERSTUDIESRESEARCHREPORTSERIESReport96.13OntheAdaptiveFiniteElementSolutionofPartialDi erentialEquationsUsingh-r-Re nementbyPJCapon&PKJimackDivisionofComputerScienceApril1996AbstractThisworkconsiderstheapplicationofthe niteelementmethodtoavarietyoftw

2、o-dimensionalpartialdi erentialequationsusingunstructuredmeshesoftriangles.Conventionalmeshre nementstrategiesinvolveestimatingthelocalerroroneachtriangleandthensubdividingthosetrianglesforwhichtheerrorexceedssomeprede nedtolerance.Whilstthisformofadaptivity(h-re nement)isgeneral

3、lyquiterobust,theworkdescribedinthispaperdemonstratesthattheadditionaluseofmeshmovementvianodalrelocation(r-re nement)cansigni cantlyenhancetheoveralleciencyoftheadaptivemethod.Moreover,theseeciencygainsmaybeobtainedverycheaplyintermsoftheextrasoftwaredevelopmentoverhead.Keywor

4、ds.FiniteElementMethods,meshadaptivity,meshquality,stability,eciency.1IntroductionInthispaperweconsidertheuseofadaptive niteelementalgorithmsforthesolutionofavarietyofsteady,elliptic-type,partialdi erentialequations(PDEs)(althoughourcomputationalexamplesaretakenfromproblemsinCom

5、putationalFluidDynamics(CFD)).Thealgorithmsthatweconsiderarebasedupontheuseofunstructuredgridsoftrianglesforproblemsintwodimensions.Suchgridsallowahighdegreeof exibilitywithrespecttoboththedomaingeometryandtheapplicationofmeshadaptivity.Thepurposeofthepaperistodemonstratethatanad

6、aptivealgorithmwhichcombinesmorethanoneapproachtomeshre nementisabletodeliverbothqualitativeandquanti ableimprovementsoveralgorithmswhichuseeitherofthere nementproceduresalone.Whilstthismaynotbeaparticularlysurprisingresult,wealsoshowhowthesegainsmaybeachievedatarelativelysmallex

7、tracostintermsofprogramminge ort.Inthenextsectionofthepaperwebrie yreviewsomeofthecommonlyusedstrategiesformeshadaptivity.Weconcentrateinparticularontheapproachesknownash-re nement(inwhichelementsmaybedividedintomorethanone,smaller,elementofthesamegeometry)andr-re nement(inwhicht

8、hemeshtopologyis xedbutthelocationsofthe

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