Generalized Normal Derivatives and Their Applications in DDMs with Nonmatching Grids and DG Methods-中国Betway体育网页登陆

摘要 Aclassofnormal-likederivativesforfunctionswithlowregularitydefinedonLipschitzdomainsareintroducedandstudied.Itisshownthatthenewnormal-likederivatives,whicharecalledthegeneralizednormalderivatives,preservethemajorprop-ertiesoftheexistingstandardnormalderivatives.Thegeneralizednormalderivativesarethenappliedtoanalyzetheconvergenceofdomaindecompositionmethods(DDMs)withnonmatchinggridsanddiscontinuousGalerkin(DG)methodsforsecond-orderel-lipticproblems.Theapproximatesolutionsgeneratedbythesemethodsstillpossesstheoptimalenergy-normerrorestimates,eveniftheexactsolutionstotheunderlyingellipticproblemsadmitverylowregularities.

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Generalized Normal Derivatives and Their Applications in DDMs with Nonmatching Grids and DG Methods

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