Superconvergence of Semidiscrete Splitting Positive Definite Mixed Finite Elements for Hyperbolic Optimal Control Problems

In this paper, we consider semidiscrete splitting positive definite mixed finite element methods for optimal control problems governed by hyperbolic equations with integral constraints. The state and costate are approximated by the lowest order Raviart-Thomas mixed rectangular finite element, and the control is approximated by piecewise constant functions. We derive some convergence and superconvergence results for the control, the state and the adjoint state. A numerical example is provided to demonstrate our theoretical results.

Numerical Modeling of the Leak through Semipermeable Walls for 2D/3D Stokes Flow: Experimental Scalability of Dual Algorithms

The paper deals with the Stokes flow subject to the threshold leak boundary conditions in two and three space dimensions. The velocity–pressure formulation leads to the inequality type problem that is approximated by the P1-bubble/P1 mixed finite elements. The resulting algebraic system is nonsmooth. It is solved by the path-following variant of the interior point method, and by the active-set implementation of the semi-smooth Newton method. Inner linear systems are solved by the preconditioned conjugate gradient method. Numerical experiments illustrate scalability of the algorithms. The novelty of this work consists in applying dual strategies for solving the problem.

A Mixed Finite Element-Based Numerical Method for Elastodynamics Considering Adhesive Interface Damage for Dynamic Fracture

The numerical solution of the elastodynamic problem with kinematic boundary conditions is considered using mixed finite elements for the space discretization and a staggered leap-frog scheme for the discretization in time. The stability of the numerical scheme is shown under the usual CFL condition. Using the general form of Robin-type boundary conditions some cases of debonding and the resulting acoustic emission are studied. The methodology presented finds applications to geophysics such as in seismic waves simulation with dynamic rupture and energy release. In this paper, we focus on problems of fracture occurring at the interface of composite materials. Our goal is to study both the mechanism of crack initiation and propagation, as well as the acoustic emission of the released structure-borne energy which may be used in structural health monitoring and prognosis applications.

Nonlinear Analysis of Frames with Shear Deformation using Higher-Order Mixed Finite Elements

Until recently, linear analysis has been considered sufficient for the static analysis of structural frames. Nonlinear effects, if included, have tended to be considered at the element level rather than at the complete structure level. However, recent changes in codes of practice have been introduced that require a more complete nonlinear analysis to be performed. While these requirements should lead to a more accurate analysis, there has been little guidance given to the type and implementation of such an analysis. Moreover, different implementations have been adopted by various commercial software. In this paper, we discuss the use of mixed finite elements for the large deflection analysis of two-dimensional frames including shear deformation. In particular, we develop a family of elements that can be combined with different nonlinear models and discuss the effects of various assumptions and approximations that are commonly used to simplify the analysis. Examples are given to illustrate the various issues discussed.