Focuses on the formulation of a number of least-squares mixed finite element schemes to solve the initial boundary value problem of a nonlinear parabolic partial differential equation. Convergence analysis; Informatio...Focuses on the formulation of a number of least-squares mixed finite element schemes to solve the initial boundary value problem of a nonlinear parabolic partial differential equation. Convergence analysis; Information on the least-squares mixed element schemes for nonlinear parabolic problem.展开更多
A mixed finite element method is developed to approximate the solution of a strongly nonlinear second-order parabolic problem. The existence and uniqueness of the approximation are demonstrated and L-2-error estimates...A mixed finite element method is developed to approximate the solution of a strongly nonlinear second-order parabolic problem. The existence and uniqueness of the approximation are demonstrated and L-2-error estimates are established for both the scalar function and the flux. Results are given for the continuous-time case.展开更多
In this paper, the Crank-Nicolson/Newton scheme for solving numerically second- order nonlinear parabolic problem is proposed. The standard Galerkin finite element method based on P2 conforming elements is used to the...In this paper, the Crank-Nicolson/Newton scheme for solving numerically second- order nonlinear parabolic problem is proposed. The standard Galerkin finite element method based on P2 conforming elements is used to the spatial discretization of the problem and the Crank-Nieolson/Newton scheme is applied to the time discretization of the resulted finite element equations. Moreover, assuming the appropriate regularity of the exact solution and the finite element solution, we obtain optimal error estimates of the fully discrete Crank- Nicolson/Newton scheme of nonlinear parabolic problem. Finally, numerical experiments are presented to show the efficient performance of the proposed scheme.展开更多
基金Major State Basic Research Program of People's Republic of China(G1999032803).
文摘Focuses on the formulation of a number of least-squares mixed finite element schemes to solve the initial boundary value problem of a nonlinear parabolic partial differential equation. Convergence analysis; Information on the least-squares mixed element schemes for nonlinear parabolic problem.
文摘A mixed finite element method is developed to approximate the solution of a strongly nonlinear second-order parabolic problem. The existence and uniqueness of the approximation are demonstrated and L-2-error estimates are established for both the scalar function and the flux. Results are given for the continuous-time case.
基金in part supported by the Distinguished Young Scholars Fund of Xinjiang Province(2013711010)NCET-13-0988the NSF of China(11271313,11271298,61163027,and 11362021)
文摘In this paper, the Crank-Nicolson/Newton scheme for solving numerically second- order nonlinear parabolic problem is proposed. The standard Galerkin finite element method based on P2 conforming elements is used to the spatial discretization of the problem and the Crank-Nieolson/Newton scheme is applied to the time discretization of the resulted finite element equations. Moreover, assuming the appropriate regularity of the exact solution and the finite element solution, we obtain optimal error estimates of the fully discrete Crank- Nicolson/Newton scheme of nonlinear parabolic problem. Finally, numerical experiments are presented to show the efficient performance of the proposed scheme.
