Nonconforming Mixed Finite Element Method for the Stationary Conduction-convection Problem
نویسندگان
چکیده
In this paper, a new stable nonconforming mixed finite element scheme is proposed for the stationary conduction-convection problem, in which a new low order Crouzeix-Raviart type nonconforming rectangular element is taken as approximation space for the velocity, the piecewise constant element for the pressure and the bilinear element for the temperature, respectively. The convergence analysis is presented and the optimal error estimates in a broken H1-norm for the velocity, L2-norm for the pressure and H1-seminorm for the temperature are derived.
منابع مشابه
Low Order Nonconforming Expanded Characteristic- Mixed Finite Element Method for the Convection- Diffusion Problem
A low order nonconforming finite element method is proposed for the convection-diffusion equations with the expanded characteristic-mixed finite element scheme. The method is a combination of characteristic approximation to handle the convection part in time and a expanded nonconforming mixed finite element spatial approximation to deal with the diffusion part. In the process, the interpolation...
متن کاملA Defect-Correction Mixed Finite Element Method for Stationary Conduction-Convection Problems
A defect-correction mixed finite element method MFEM for solving the stationary conductionconvection problems in two-dimension is given. In this method, we solve the nonlinear equations with an added artificial viscosity term on a grid and correct this solution on the same grid using a linearized defect-correction technique. The stability is given and the error analysis in L2 and H1-norm of u, ...
متن کاملA New Characteristic Nonconforming Mixed Finite Element Scheme for Convection-Dominated Diffusion Problem
A characteristic nonconforming mixed finite element method (MFEM) is proposed for the convection-dominated diffusion problem based on a new mixed variational formulation. The optimal order error estimates for both the original variable u and the auxiliary variable σ with respect to the space are obtained by employing some typical characters of the interpolation operator instead of the mixed (or...
متن کاملA Hybridized Crouziex-Raviart Nonconforming Finite Element and Discontinuous Galerkin Method for a Two-Phase Flow in the Porous Media
In this study, we present a numerical solution for the two-phase incompressible flow in the porous media under isothermal condition using a hybrid of the linear lower-order nonconforming finite element and the interior penalty discontinuous Galerkin (DG) method. This hybridization is developed for the first time in the two-phase modeling and considered as the main novelty of this research.The p...
متن کاملA Finite Element Variational Multiscale Method Based on Two Local Gauss Integrations for Stationary Conduction-Convection Problems
A new finite element variational multiscale VMS method based on two local Gauss integrations is proposed and analyzed for the stationary conduction-convection problems. The valuable feature of our method is that the action of stabilization operators can be performed locally at the element level with minimal additional cost. The theory analysis shows that our method is stable and has a good prec...
متن کامل