Discrete and Continuous Dynamical Systems - B · 2006 · 40 citations · 0 references
ComputingComputational EngineeringMechanical EngineeringComputational MechanicsFinite Element AnalysisFinite Element MethodsConvergence AnalysisError EstimationFinite Element DiscretizationFinite Element FormulationNavier-stokes EquationsNumerical StabilityA Posteriori Error EstimatesElement FormulationError Estimation For Finite Element SolutionsFinite Element ModelingQuadrilateral ElementsStabilized FormulationsTriangular Elements
In this article, a locally stabilized finite element formulation of the two-dimensional Navier-Stokes problem is used. A macroelement condition which provides the stability of the $Q_1-P_0$ quadrilateral element and the $P_1-P_0$ triangular element is introduced. Moreover, the $H^1$ and $L^2$-error estimates of optimal order for finite element solution $(u_h,p_h)$ are analyzed. Finally, a uniform $H^1$ and $L^2$-error estimates of optimal order for finite element solution $(u_h,p_h)$ is obtained if the uniqueness condition is satisfied.