A priori error estimation for the dual mixed finite element method of the elastodynamic problem in a polygonal domain, II
نویسندگان
چکیده
In this paper we analyze a new dual mixed formulation of the elastodynamic system in polygonal domains. In this formulation the symmetry of the strain tensor is relaxed by the rotational of the displacement. For the time discretization of this new dual mixed formulation, we use an explicit scheme. After the analysis of stability of the fully discrete scheme, L∞ in time, L2 in space a priori error estimates are derived for the approximation of the displacement, the strain, the pressure and the rotational. Numerical experiments confirm our theoretical predictions. MSC: 65M60; 65M15; 65M50
منابع مشابه
Optimal order finite element approximation for a hyperbolic integro-differential equation
Semidiscrete finite element approximation of a hyperbolic type integro-differential equation is studied. The model problem is treated as the wave equation which is perturbed with a memory term. Stability estimates are obtained for a slightly more general problem. These, based on energy method, are used to prove optimal order a priori error estimates.
متن کاملVARIATIONAL DISCRETIZATION AND MIXED METHODS FOR SEMILINEAR PARABOLIC OPTIMAL CONTROL PROBLEMS WITH INTEGRAL CONSTRAINT
The aim of this work is to investigate the variational discretization and mixed finite element methods for optimal control problem governed by semi linear parabolic equations with integral constraint. The state and co-state are approximated by the lowest order Raviart-Thomas mixed finite element spaces and the control is not discreted. Optimal error estimates in L2 are established for the state...
متن کاملA Priori and A Posteriori Error Estimations for the Dual Mixed Finite Element Method of the Navier-Stokes Problem
This article is concerned with a dual mixed formulation of the Navier-Stokes system in a polygonal domain of the plane with Dirichlet boundary conditions and its numerical approximation. The gradient tensor, a quantity of practical interest, is introduced as a new unknown. The problem is then approximated by a mixed finite element method. Quasi-optimal a priori error estimates are obtained. The...
متن کاملThe Effects of Newmark Method Parameters on Errors in Dynamic Extended Finite Element Method Using Response Surface Method
The Newmark method is an effective method for numerical time integration in dynamic problems. The results of Newmark method are function of its parameters (β, γ and ∆t). In this paper, a stationary mode I dynamic crack problem is coded in extended finite element method )XFEM( framework in Matlab software and results are verified with analytical solution. This paper focuses on effects of main pa...
متن کاملWeighted L-norm a Posteriori Error Estimation of Fem in Polygons
In this paper, we generalize well-known results for the L2-norm a posteriori error estimation of finite element methods applied to linear elliptic problems in convex polygonal domains to the case where the polygons are nonconvex. An important factor in our analysis is the investigation of a suitable dual problem whose solution, due to the non-convexity of the domain, may exhibit corner singular...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید
ثبت ناماگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید
ورودعنوان ژورنال:
- J. Computational Applied Mathematics
دوره 235 شماره
صفحات -
تاریخ انتشار 2009