A Finite Difference Scheme on a Priori Adapted Meshes for a Singularly Perturbed Parabolic Convection-Diffusion Equation-中国期刊网

摘要 Aboundaryvalueproblemisconsideredforasingularlyperturbedparabolicconvection-diffusionequation;weconstructafinitedifferenceschemeonapriori(se-quentially)adaptedmeshesandstudyitsconvergence.Theschemeonaprioriadaptedmeshesisconstructedusingamajorantfunctionforthesingularcomponentofthediscretesolution,whichallowsustofindaprioriasubdomainwherethecomputedsolutionrequiresafurtherimprovement.Thissubdomainisdefinedbytheperturbationparameterε,thestep-sizeofauniformmeshinx,andalsobytherequiredaccuracyofthediscretesolutionandtheprescribednumberofrefinementiterationsKforim-provingthesolution.Tosolvethediscreteproblemsaimedattheimprovementofthesolution,weuseuniformmeshesonthesubdomains.Theerrorofthenumericalso-lutiondependsweaklyontheparameterε.Theschemeconvergesalmostε-uniformly,precisely,undertheconditionN~(-1)=o(ε~v),whereNdenotesthenumberofnodesinthespatialmesh,andthevaluev=v(K)canbechosenarbitrarilysmallforsuitableK.

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A Finite Difference Scheme on a Priori Adapted Meshes for a Singularly Perturbed Parabolic Convection-Diffusion Equation

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A Finite Difference Scheme on a Priori Adapted Meshes for a Singularly Perturbed Parabolic Convection-Diffusion Equation

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