Finite element methods in which two spaces are used to approximate two different variables receive the general denomination of mixed methods. In some cases, the second variable is introduced in the formulation of the problem because of its physical interest and it is usually related with some derivatives of the original variable. This is the case, for example, in the elasticity equations, where...

Modeling of crack propagation by a finite element method under mixed mode conditions is of prime importance in the fracture mechanics. This article describes an application of finite element method to the analysis of mixed mode crack growth in linear elastic fracture mechanics. Crack - growth process is simulated by an incremental crack-extension analysis based on the maximum principal stress c...

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...

• Mixed methods for elastodynamics with weak symmetry. • Mixed finite elements for elasticity on quadrilateral meshes. • Finite element differential forms on curvilinear cubic meshes and their approximation properties. Numer. • Nonconforming tetrahedral mixed finite elements for elasticity. • Mixed finite element approximation of the vector Laplacian with Dirichlet boundary conditions. Math. • ...

Displacement finite element models of various beam theories have been developed traditionally using conventional finite element basis functions (i.e., cubic Hermite, equi-spaced Lagrange interpolation functions, or spectral/hp Legendre functions). Various finite element models of beams differ from each other in the choice of the interpolation functions used for the transverse deflection w, tota...

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...

We develop a new mixed formulation for the numerical solution of second-order elliptic problems. This new formulation expands the standard mixed formulation in the sense that three variables are explicitly treated: the scalar unknown, its gradient, and its ux (the coeecient times the gradient). Based on this formulation, mixed nite element approximations of the second-order elliptic problems ar...