This paper studies a low order mixed finite element method （FEM） for nonstationary incompressible Navier-Stokes equations. The velocity and pressure are approximated by the nonconforming constrained Q1^4ot element a...This paper studies a low order mixed finite element method （FEM） for nonstationary incompressible Navier-Stokes equations. The velocity and pressure are approximated by the nonconforming constrained Q1^4ot element and the piecewise constant, respectively. The superconvergent error estimates of the velocity in the broken H^1-norm and the pressure in the L^2-norm are obtained respectively when the exact solutions are reasonably smooth. A numerical experiment is carried out to confirm the theoretical results.展开更多
Both numerical simulation and theoretical analysis of seawater intrusion in coastal regions are of great theoretical importance in environmental sciences. The mathematical model can be described as a coupled system of...Both numerical simulation and theoretical analysis of seawater intrusion in coastal regions are of great theoretical importance in environmental sciences. The mathematical model can be described as a coupled system of three dimensional nonlinear partial differential equations with initial-boundary value problems. In this paper, according to the actual conditions of molecular and three-dimensional characteristic of the problem, we construct the characteristic finite element alternating-direction schemes which can be divided into three continuous one-dimensional problems. By making use of tensor product algorithm, and priori estimation theory and techniques, the optimal order estimates in H1 norm are derived for the error in the approximate solution.展开更多
In this paper, two new nonconforming hexagonal elements are presented, which are based on the trilinear function space Q1^（3） and are edge-oriented, analogical to the case of the rotated Q1 quadrilateral element. A ...In this paper, two new nonconforming hexagonal elements are presented, which are based on the trilinear function space Q1^（3） and are edge-oriented, analogical to the case of the rotated Q1 quadrilateral element. A priori error estimates are given to show that the new elements achieve first-order accuracy in the energy norm and second-order accuracy in the L^2 norm. This theoretical result is confirmed by the numerical tests.展开更多
基金Project supported by the National Natural Science Foundation of China(No.11271340)
文摘This paper studies a low order mixed finite element method （FEM） for nonstationary incompressible Navier-Stokes equations. The velocity and pressure are approximated by the nonconforming constrained Q1^4ot element and the piecewise constant, respectively. The superconvergent error estimates of the velocity in the broken H^1-norm and the pressure in the L^2-norm are obtained respectively when the exact solutions are reasonably smooth. A numerical experiment is carried out to confirm the theoretical results.
基金the National Natural Science Foundation of China (No.40023001 and 40075015)KZCX2-208 of the Chinese Academy of Sciences.
文摘Both numerical simulation and theoretical analysis of seawater intrusion in coastal regions are of great theoretical importance in environmental sciences. The mathematical model can be described as a coupled system of three dimensional nonlinear partial differential equations with initial-boundary value problems. In this paper, according to the actual conditions of molecular and three-dimensional characteristic of the problem, we construct the characteristic finite element alternating-direction schemes which can be divided into three continuous one-dimensional problems. By making use of tensor product algorithm, and priori estimation theory and techniques, the optimal order estimates in H1 norm are derived for the error in the approximate solution.
基金The research is supported by National Basic Research Program of china(No. 2005CB321702)National Natural Science Foundation of china(No. 10431050)
文摘In this paper, two new nonconforming hexagonal elements are presented, which are based on the trilinear function space Q1^（3） and are edge-oriented, analogical to the case of the rotated Q1 quadrilateral element. A priori error estimates are given to show that the new elements achieve first-order accuracy in the energy norm and second-order accuracy in the L^2 norm. This theoretical result is confirmed by the numerical tests.
