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Mixed finite element method
About: Mixed finite element method is a research topic. Over the lifetime, 22284 publications have been published within this topic receiving 614167 citations.
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TL;DR: An efficient and fully computable a posteriori error bound is derived for the discrete duality finite volume discretization of the Laplace equation on very general two-dimensional meshes.
Abstract: An efficient and fully computable a posteriori error bound is derived for the discrete duality finite volume discretization of the Laplace equation on very general two-dimensional meshes. The main ingredients are the equivalence of this method with a finite element like scheme and tools from the finite element framework. Numerical tests are performed with a stiff solution on highly nonconforming locally refined meshes and with a singular solution on triangular meshes.
9 citations
01 Jan 1988
TL;DR: A survey of the advances in the theory and practice of the p and h-p versions of the finite element method can be found in this paper, where the authors give an extensive list of references related to recent results of this new approach.
Abstract: The paper gives the survey of the advances in the theory and practice of the p and h-p versions of the finite element method. It gives the extensive list of references related to recent results of this new approach.
9 citations
TL;DR: In this paper, a straight beam element based on curvature is proposed to eliminate the shear locking phenomenon, which is also applicable to the analysis of both thin and thick straight beams.
Abstract: The formulation of a straight beam element to eliminate the shear locking phenomenon is presented. The element is based on curvature so that the bending energy is fully represented, and the shear strain energy is incorporated into the formulation by the equilibrium equation. Four examples are chosen to verify the concept of the element employed and its capability of the analysis. The solutions obtained reveal that the element describes the behaviour of the straight beam quite exactly and efficiently, showing no locking and that it is also applicable to the analysis of both thin and thick straight beams.
9 citations
TL;DR: The bases obtained by the formation of null basis for finite element model discretized as rectangular bending elements correspond to highly sparse and narrowly banded flexibility matrices and such bases can be considered as an efficient tool for optimal analysis of structures.
Abstract: Purpose – This paper seeks to present an efficient algorithm for the formation of null basis for finite element model discretized as rectangular bending elements. The bases obtained by this algorithm correspond to highly sparse and narrowly banded flexibility matrices and such bases can be considered as an efficient tool for optimal analysis of structures.Design/methodology/approach – In the present method, two graphs are associated with finite element mesh consisting of an “interface graph” and an “associate digraph”. The underlying subgraphs of the self‐equilibrating systems (SESs) (null vectors) are obtained by graph theoretical approaches forming a null basis. Application of unit loads (moments) at the end of the generator of each subgraph results in the corresponding null vector.Findings – In the present hybrid method, graph theory is used for the formation of null vectors as far as it is possible and then algebraic method is utilized to find the complementary part of the null basis.Originality/value...
9 citations
TL;DR: In this paper, a coupled finite element-finite volume method for numerical approximation of singularly perturbed convection-diffusion problems is presented, which is based on the node-centred method and a standard continuous finite element approximation of the diffusive term.
Abstract: In this paper we present and analyse a coupled finite element-finite volume method for the numerical approximation of singularly perturbed convection-diffusion problems. The idea is to couple a discretization for the convective term, based on the finite volume (node-centred) method, and a standard continuous finite element approximation of the diffusive term. Such a method preserves conservation, fulfils consistency and enhances stability.
9 citations