Gradient schemes is a framework that enables the unified convergence analysis of many numerical methods for elliptic and parabolic partial differential equations: conforming and non-conforming Finite Element, Mixed Finite Element and Finite Volume methods. We show here that this framework can be applied to a family of degenerate non-linear parabolic equations (which contain in particular the Ri...

ABSTRACT 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 L are established for t...

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...

This paper presents mixed finite element methods of higher-order for a simplified Signorini problem and an idealized frictional problem. The discretization is based on a mixed variational formulation proposed by Haslinger et al. which is extended to higher-order finite elements. To guarantee the unique existence of the solution of the mixed method, a discrete inf-sup condition is proven. Approx...

We investigate a mortar technique for mixed finite element approximations of class domain decomposition saddle point problems on nonmatching grids in which the variable associated with essential boundary condition, referred to as flux, is chosen coupling variable. It plays role Lagrange multiplier impose weakly continuity natural condition. The flux-mortar incorporated use discrete extension op...

We apply high-order mixed finite element discretization techniques and their associated preconditioned iterative solvers to the Variable Eddington Factor (VEF) equations in two spatial dimensions. The VEF discretizations are coupled a Discontinuous Galerkin (DG) of discrete ordinates transport equation form effective linear algorithms that compatible with (curved) meshes. This combination is mo...