This paper presents a mixed variational formulation and its discretization by finite elements of higher-order for the Signorini problem with Tresca friction. To guarantee the unique existence of the solution to the discrete mixed problem, a discrete inf-sup condition is proved. Moreover, a solution scheme based on the dual formulation of the problem is proposed. Numerical results confirm the th...

In this paper two research studies by Eells (2010) and Edwards (2010) evaluating case formulation and therapist responsiveness are summarized and critically evaluated. The central themes abstracted from these studies are subsequently articulated and integrated with existing research on the philosophical and theoretical competencies, clinical competencies, and quantitative competencies needed fo...

The stress-velocity formulation of the stationary Stokes problem allows an Arnold–Winther mixed finite element formulation with some superconvergent reconstruction of the velocity. This local postprocessing gives rise to two reliable a posteriori error estimators which recover optimal convergence order for the stress error estimates. The theoretical results are investigated in numerical benchma...

We perform a systematic multiscale analysis for the 2-D incompressible Euler equation with rapidly oscillating initial data using a Lagrangian approach. The Lagrangian formulation enables us to capture the propagation of the multiscale solution in a natural way. By making an appropriate multiscale expansion in the vorticity-stream function formulation, we derive a well-posed homogenized equatio...

This chapter focuses on stochastic control and decision processes that occur in a variety of theoretical and applied contexts, such as statistical decision problems, stochastic dynamic programming problems, gambling processes, optimal stopping problems, stochastic adaptive control processes, and so on. It has long been recognized that these are all mathematically closely related. That being the...

We study theoretically and experimentally the mechanisms of nonlinear and nonequilibrium dynamics in geomaterials through dynamic acoustoelasticity testing. In the proposed theoretical formulation, the classical theory of nonlinear elasticity is extended to include the effects of conditioning. This formulation is adapted to the context of dynamic acoustoelasticity testing in which a low-frequen...

Proper orthogonal decomposition (POD) method has been successfully used in the reduced-order modeling of complex systems. In this paper, we extend the applications of POD method, i.e., combine the classical finite volume element (FVE) method with the POD method to obtain a reduced-order FVE formulation with lower dimensions and sufficiently high accuracy for two-dimensional solute transport pro...

A linear, aeroelastic analysis of a low aspect ratio swept back trapezoidal wing modeled as a cantilever plate is presented. An analytical and numerical formulation for both the aerodynamic forcing and structural response of the wing was developed. The analytical model uses a three dimensional time domain vortex lattice aerodynamic method. A Rayleigh-Ritz approach has been used to transfer equa...