in recent years, the application of composite materials in aircraft and space vehicle structural components has become increasingly popular. preventing failure of composite structural systems has been an important issue in engineering design. due to the lack of through-the-thickness reinforcement, structures made from laminated composite materials and adhesively bonded joints are highly suscept...

We introduce a new class of higher order mixed finite volume methods for elliptic problems. We start from the usual way of changing the given equation into a mixed system using the Darcy’s law, u = −K∇p. By integrating the system of equations with some judiciously chosen test spaces on each element, we define new mixed finite volume methods of higher order. We show that these new schemes are eq...

In this article, an adaptive least-squares mixed finite element method is studied for pseudo-parabolic integro-differential equations. The solutions of least-squares mixed weak formulation and mixed finite element are proved. A posteriori error estimator is constructed based on the least-squares functional and the posteriori errors are obtained. Keywords—Pseudo-parabolic integro-differential eq...

Three-dimensional enriched finite elements are used to compute mixed-mode stress intensity factors (SIFs) for three-dimensional cracks in elastic functionally graded materials (FGMs) that are subject to general mixed-mode loading. The method, which advantageously does not require special mesh configuration/modifications and post-processing of finite element results, is an enhancement of previou...

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....

In this work we present a theoretical analysis for a residual-type error estimator for locally conservative mixed methods. This estimator was first introduced by Braess and Verfürth for the Raviart–Thomas mixed finite element method working in mesh-dependent norms. We improve and extend their results to cover any locally conservative mixed method under minimal assumptions, in particular, avoidi...

In this paper we analyze the finite element discretization for the first-order system least squares mixed model for the second-order elliptic problem by means of using nonconforming and conforming elements to approximate displacement and stress, respectively. Moreover, on arbitrary regular quadrilaterals, we propose new variants of both the rotated Q1 nonconforming element and the lowest-order ...

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...