两类方程的有限体积元方法-计算数学专业毕业论文.docx

两类方程的有限体积元方法李少芳山东师范大学数学科学学院,济南,山东,250014摘 要本文首先考虑如下二维对流扩散问题ut+∇·(bu−D∇u)=f, (x,t)∈Ω×J,u=0, (x,t)∈Γ×J,u(x,0)=u0(x), x∈Ω,,特征间断有限体积元方法既具有间断有限体积元方法高精度、高并行性、空间构造简单等的优点,同时也有特征线方法格式的稳定性好、,,在第二章,我们采用修正的特征间断有限体积元方法,通过在对偶的时空单元上积分,使方法不但具有特征间断有限体积元方法的优点,同时保持了间断有限体积元方法局部质量守恒的特性,同时我们进行了离散H1模和L2模误差分析,ut+∇p−γ∆u=g(x,t), (x,t)∈Ω×I,∇·u=0, (x,t)∈Ω×I,u=0, (x,t)∈Γ×I,u=u0(x), x∈,同时计算格式简单,运算量小,,利用流函数-涡度的方法,:对流扩散方程,守恒特征间断有限体积元,非定常stokes问题,有限体积元方法,误差估计中图分类号:,ShandongNormalUniversityJinan,Shandong,250014ABSTRACTInthispaper,thefollowingtwo-dimensionalconvection-diffusioninitialbound-aryproblemut+∇·(bu−D∇u)=f, (x,t)∈Ω×J,u=0, (x,t)∈Γ×J,u(x,0)=u0(x), x∈Ω,,characteristicdiscontinuousfinitevolumemethod,whichnotonlypossesstheadvantagesofdiscontinuousfinitevolumemethod,forexample,uracy,parallelizabilityandsimplicityofspaceconstruc-tion,italsoinheritssomefeaturesofcharacteristicmethod:-umemethoddoesnothavetheconservationofnature,Therefore,inthesecondchapter,wefirstsimulatethemodifiedcharacteristicdiscontinuousfinitevolumeelementmethod,byintegrallinginthedualspaceunit,themethodnotonlyhasthecharacteristicsofdiscontinuousfinitevolumeelementmethod,whilemaintain-ingthediscontinuousfinitevolumeelementmethodforthecharacteristicsoflocalconservationofmass,bymakingthenumericalanalysis,weobtaintheoptimalerrorestimatesof|||·|||1,h-,thefollowingstokesequationisconsidered.ut+∇p−γ∆u=g(x,t), (x,t)∈Ω×I,∇·u=0, (x,t)∈Ω×I,