Error analysis of a fully discrete finite element method for variable density incompressible flows in two dimensions
Wentao Cai, Buyang Li, Ying Li
Abstract
An error estimate is presented for a fully discrete, linearized and stabilized finite element method for solving the coupled system of nonlinear hyperbolic and parabolic equations describing incompressible flow with variable density in a two-dimensional convex polygon. In particular, the error of the numerical solution is split into the temporal and spatial components, separately. The temporal error is estimated by applying discrete maximal L p -regularity of time-dependent Stokes equations, and the spatial error is estimated by using energy techniques based on the uniform regularity of the solutions given by semi-discretization in time.
Topics & Concepts
MathematicsDiscretizationFinite element methodMathematical analysisCompressibilityNonlinear systemTemporal discretizationRegular polygonApplied mathematicsPressure-correction methodPolygon (computer graphics)GeometryQuantum mechanicsFrame (networking)EngineeringPhysicsThermodynamicsAerospace engineeringComputer scienceTelecommunicationsAdvanced Numerical Methods in Computational MathematicsComputational Fluid Dynamics and AerodynamicsNumerical methods in engineering