Jason S. Howell

Inf–sup conditions for twofold saddle point problems

Necessary and sufficient conditions for existence and uniqueness of solutions are developed for twofold saddle point problems which arise in mixed formulations of problems in continuum mechanics. This work extends the classical saddle point theory to accommodate nonlinear constitutive relations and the twofold saddle structure. Application to problems in incompressible fluid mechanics employing symmetric tensor finite elements for the stress approximation is presented.

Dual-mixed finite element approximation of Stokes and nonlinear Stokes problems using trace-free velocity gradients

In this work a finite element method for a dual-mixed approximation of Stokes and nonlinear Stokes problems is studied. The dual-mixed structure, which yields a twofold saddle point problem, arises in a formulation of this problem through the introduction of unknown variables with relevant physical meaning. The method approximates the velocity, its gradient, and the total stress tensor, but avoids the explicit computation of the pressure, which can be recovered through a simple postprocessing technique. This method improves an existing approach for these problems and uses Raviart-Thomas elements and discontinuous piecewise polynomials for approximating the unknowns. Existence, uniqueness, and error results for the method are given, and numerical experiments that exhibit the reduced computational cost of this approach are presented.

A two-parameter defect-correction method for computation of steady-state viscoelastic fluid flow

The numerical simulation of viscoelastic fluid flow becomes more difficult as a physical parameter, the Weissenberg number, increases. Specifically, at a Weissenberg number larger than a critical value, the iterative nonlinear solver fails to converge. In this paper a two-parameter defect-correction method for viscoelastic fluid flow is presented and analyzed. In the defect step the Weissenberg number is artificially reduced to solve a stable nonlinear problem. The approximation is then improved in the correction step using a linearized correction iteration. Numerical experiments support the theoretical results and demonstrate the effectiveness of the method.

Partitioned Time Stepping for a Parabolic Two Domain Problem

There have been many numerical simulations but few analytical results of stability and accuracy of algorithms for computational modeling of fluid-fluid and fluid-structure interaction problems, where two domains corresponding to different fluids (ocean-atmosphere) or a fluid and deformable solid (blood flow) are separated by an interface. As a simplified model of the first examples, this report considers two heat equations in

Dual-mixed finite element methods for the Navier-Stokes equations

\Omega_1,\Omega_2\subset\mathbb{R}^2

Decoupled Time Stepping Methods for Fluid-Fluid Interaction

adjoined by an interface

A Functional Approach to Solubility Parameter Computations

I=\Omega_1\cap\Omega_2\subset\mathbb{R}

A General Polynomial Sieve

. The heat equations are coupled by a condition that allows energy to pass back and forth across the interface

A Cantilevered Extensible Beam in Axial Flow: Semigroup Well-posedness and Postflutter Regimes

I

Prestructuring sparse matrices with dense rows and columns via null space methods: Prestructuring sparse matrices with dense rows

while preserving the total global energy of the monolithic, coupled problem. To compute approximate solutions to the above problem only using subdomain solvers, two first-order in time, fully discrete methods are presented. The methods consist of an implicit-explicit approach, in which the action across