Ohannes A. Karakashian

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Several a posteriori error estimators are introduced and analyzed for a discontinuous Galerkin formulation of a model second-order elliptic problem. In addition to residual-type estimators, we introduce some estimators that are couched in the ideas and techniques of domain decomposition. Results of numerical experiments are presented.
Abstract. A residual type a posteriori error estimator is introduced and analyzed for a discontinuous Galerkin formulation of a model second-order elliptic problem with Dirichlet-Neumann type boundary conditions. An adaptive algorithm using this estimator together with specific marking and refinement strategies is constructed and shown to achieve any(More)
We approximate the solutions of an initialand boundary-value problem for nonlinear Schrödinger equations (with emphasis on the ‘cubic’ nonlinearity) by two fully discrete finite element schemes based on the standard Galerkin method in space and two implicit, Crank–Nicolson-type second-order accurate temporal discretizations. For both schemes we study the(More)
We consider the initial-value problem for the radially symmetric nonlinear Schrödinger equation with cubic nonlinearity (NLS) in d = 2 and 3 space dimensions. To approximate smooth solutions of this problem, we construct and analyze a numerical method based on a standard Galerkin finite element spatial discretization with piecewise linear, continuous(More)
1Department of Mathematics and Applied Research Laboratory, The Pennsylvania State University, University Park, PA 16802 U.S.A. 2Mathematics Department, National Technical University, Zographou, 15780 Athens, Greece, and Institute of Applied and Computational Mathematics, F. O.R. T.H., Greece 3Department of Mathematics, University of Tennessee, Knoxville,(More)
Fully discrete discontinuous Galerkin methods with variable meshes in time are developed for the fourth order Cahn-Hilliard equation arising from phase transition in materials science. The methods are formulated and analyzed in both two and three dimensions, and are proved to give optimal order error bounds. This coupled with the flexibility of the methods(More)
Abstract. We construct, analyze and numerically validate a class of conservative, discontinuous Galerkin schemes for the Generalized Korteweg-de Vries equation. Up to round-off error, these schemes preserve discrete versions of the first two invariants (the integral of the solution, usually identified with the mass, and the L–norm) of the continuous(More)
We consider approximating the solution of the initial and boundary value problem for the Navier-Stokes equations in bounded twoand three-dimensional domains using a nonstandard Galerkin (finite element) method for the space discretization and the third order accurate, three-step backward differentiation method (coupled with extrapolation for the nonlinear(More)