A least-squares mixed finite element (LSMFE) method for the numerical solution of fourth order parabolic problems analyzed and developed in this paper. The Ciarlet-Raviart mixed finite element space is used to approximate. The a posteriori error estimator which is needed in the adaptive refinement algorithm is proposed. The local evaluation of the least-squares functional serves as a posteriori...

We will investigate the adaptive mixed finite element methods for parabolic optimal control problems. The state and the costate are approximated by the lowest-order Raviart-Thomas mixed finite element spaces, and the control is approximated by piecewise constant elements. We derive a posteriori error estimates of themixed finite element solutions for optimal control problems. Such a posteriori ...

In this paper we propose a method for improving the convergence rate of the mixed finite element approximations for the Stokes eigenvalue problem. It is based on a postprocessing strategy that consists of solving an additional Stokes source problem on an augmented mixed finite element space which can be constructed either by refining the mesh or by using the same mesh but increasing the order o...

where ∇ and ∇· are the gradient and divergence operators, Ω ⊂ R is an open bounded cubic domain with boundary Γ, n indicates the outward unit normal vector along Γ, A−1 = (αij)3×3 is a full positive definite matrix uniformly in Ω. Mixed finite element methods [1] should be employed to discretize the system (1.1). The main content of this paper is to present an analysis for the extrapolation of ...

Abstract: The vibration analysis of horizontally curved beams is generally led to higher order shape functions using direct finite element method, resulting in more time-consuming computation process. In this paper, the weak-form mixed finite element method was used to reduce the order of shape functions. The shape functions were first considered linear which did not provide adequate accuracy....