Gradient Schemes for Linear and Non-linear Elasticity Equations

The Gradient Scheme framework provides a unified analysis setting for many different families of numerical methods for diffusion equations. We show in this paper that the Gradient Scheme framework can be adapted to elasticity equations, and provides error estimates for linear elasticity and convergence results for non-linear elasticity. We also establish that several classical and modern numerical methods for elasticity are embedded in the Gradient Scheme framework, which allows us to obtain convergence results for these methods in cases where the solution does not satisfy the full $H^2$-regularity or for non-linear models

"Disability and Returns to Education in a Developing Country"

In this paper, we estimate wage returns to investment in education for persons with disabilities in Nepal, using information on the timing of being impaired during school-age years as identifying instrumental variables for years of schooling. We employ unique data collected from persons with hearing, physical, and visual impairments as well as nationally representative survey data from the Nepal Living Standard Survey 2003/2004 (NLSS II). After controlling for endogeneity bias arising from schooling decisions as well as sample selection bias due to endogenous labor participation, the estimated rate of returns to education is very high among persons with disabilities, ranging from 19.4 to 33.2%. The coexistence of these high returns to education and limited years of schooling suggest that supply side constraints in education to accommodate persons with disabilities and/or there are credit market imperfections. Policies to eliminate these barriers will mitigate poverty among persons with disabilities, the largest minority group in the world.

Application of projection algorithms to differential equations: boundary value problems

The Douglas-Rachford method has been employed successfully to solve many kinds of non-convex feasibility problems. In particular, recent research has shown surprising stability for the method when it is applied to finding the intersections of hypersurfaces. Motivated by these discoveries, we reformulate a second order boundary valued problem (BVP) as a feasibility problem where the sets are hypersurfaces. We show that such a problem may always be reformulated as a feasibility problem on no more than three sets and is well-suited to parallelization. We explore the stability of the method by applying it to several examples of BVPs, including cases where the traditional Newton's method fails