The Integral Mean Non-overlapping Domain Decomposition Method For Viscoelastic Fluid Flow Mathematical Model

The viscoelastic fluid flow obeying an Oldroyd B type constitutive law is a special attention question. At present, V-cycle multi-grid method, least-square mixed finite element method and mixed finite element method and so on have been used to solve the viscoelastic fluid flow obeying an Oldroyd B type constitutive law by some researchers.In this paper, we research integral mean non-overlapping domain decomposition method for Oldroyd B type constitutive mathematical model. This method uses simple explicit flux calculation on the inter-domain boundaries and implicit Galerkin method in the sub-domains. To improve higher order accuracy with respect to H, we use ectrapolation-integral mean parallel domain decomposition method to present the viscoelastic fluid flow the finite scheme.In the first chapter, we briefly introduce the background and the status of recent researches of the finite element method, and the main problem which we discuss.In the second chapter, we introduce the domain decomposition method, present integral mean non-overlapping parallel Galerkin finite element value scheme and ectrapolation-integral mean non-overlapping parallel Galerkin value scheme for viscoelastic fluid flow obeying an Oldroyd B type constitutive finite element law model.In the third chapter, we analysis the convergence of integral mean numerical value scheme, and get theorem of error estimate.In the fouth chapter, we analysis the convergence of ectrapolation-integral mean numerical value scheme, and get theorem of error estimate.