An elliptic partial differential equation may be formulated in different but equivalent ways, and the mixed finite element methods derived from these formulations have different properties. We give general error estimates for two such methods, which are always optimal for the Raviart– Thomas elements, but which are suboptimal for the Brezzi–Douglas–Marini elements in one of the methods. Computa...

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 ...

A physically based duality theory for first order elliptic systems is shorn to be of central importance in connection with the Galerkin finite element solution of these systems. Using this theory in conjunction with a certain hypothesis concerning approximation spaces, optimal error estimates for Galerkin type approximations are demonstrated. An example of a grid which satisfies the hypothesis ...

in the present study, a spectral finite element method is developed for free and forced transverse vibration of levy-type moderately thick rectangular orthotropic plates based on first-order shear deformation theory. levy solution assumption was used to convert the two-dimensional problem into a one-dimensional problem. in the first step, the governing out-of-plane differential equations are tr...

Plant tissue has a complex cellular structure which is an aggregate of individual cells bonded by middle lamella. During drying processes, plant tissue undergoes extreme deformations which are mainly driven by moisture removal and turgor loss. Numerical modelling of this problem becomes challenging when conventional grid-based modelling techniques such as finite element and finite difference me...

Small deformations of a viscoelastic body are considered through the linear Maxwell and Kelvin-Voigt models in the quasi-static equilibrium. A robust mixed finite element method, enforcing the symmetry of the stress tensor weakly, is proposed for these equations on simplicial tessellations in two and three dimensions. A priori error estimates are derived and numerical experiments presented. The...

We derive new a-priori and a-posteriori error estimates for mixed nite element discretizations of second-order elliptic problems with general Robin boundary conditions, parameterized by a non-negative and piecewise constant function ε ≥ 0. The estimates are robust over several orders of magnitude of ε, ranging from pure Dirichlet conditions to pure Neumann conditions. A series of numerical expe...

The hybridization technique is applied to replace the macro-hybrid mixed finite element problem for the diffusion equation by the equivalent cell-based formulation. The underlying algebraic system is condensed by eliminating the degrees of freedom which represent the interface flux and cell pressure variables to the system containing the Lagrange multipliers variables. An approach to the numeri...

The balancing domain decomposition method for mixed finite elements by Cowsar, Mandel, and Wheeler is extended to the case of mortar mixed finite elements on non-matching multiblock grids. The algorithm involves an iterative solution of a mortar interface problem with one local Dirichlet solve and one local Neumann solve per subdomain on each iteration. A coarse solve is used to guarantee that ...

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...