Ohannes A. Karakashian

TL;DR: Several a posteriori error estimators are introduced and analyzed for a discontinuous Galerkin formulation of a model second-order elliptic problem and some estimators that are couched in the ideas and techniques of domain decomposition are introduced.

TL;DR: This work approximate the solutions of an initial- and boundary-value problem for nonlinear Schrödinger equations by two fully discrete finite element schemes based on the standard Galerkin method in space and two implicit schemes, each of which proves L2 error bounds of optimal order of accuracy.

TL;DR: A class of fully discrete schemes for the numerical simulation of solutions of the periodic initial-value problem for a class of generalized Korteweg-de Vries equations is analysed, implemented and tested and the information gleaned is used in the investigation of the instability of the solitary-wave solutions of a certain class of these equations.

TL;DR: In this article, a nonconforming finite element approximations to solutions of the Stokes equations are constructed and the optimal rates of convergence are proved for the velocity and pressure approximation.

TL;DR: The convergence of the discontinuous Galerkin method for the nonlinear (cubic) Schrodinger equation is analyzed and the existence of the resulting approximations and optimal order error estimates in L∞(L 2 ).