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A space-time finite element method for the nonlinear Schrödinger equation: the discontinuous Galerkin method

Authors: Ohannes Karakashian and Charalambos Makridakis
Journal: Math. Comp. 67 (1998), 479-499
MSC (1991): Primary 65M60, 65M12
MathSciNet review: 1459390
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Abstract: The convergence of the discontinuous Galerkin method for the nonlinear (cubic) Schrödinger equation is analyzed in this paper. We show the existence of the resulting approximations and prove optimal order error estimates in $L^{\infty }(L^{2} ) .$ These estimates are valid under weak restrictions on the space-time mesh.

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Additional Information

Ohannes Karakashian
Affiliation: Department of Mathematics, University of Tennessee, Knoxville, Tennessee 37966

Charalambos Makridakis
Affiliation: Department of Mathematics, University of Crete, 714 09 Heraklion, Crete, Greece
MR Author ID: 289627

Received by editor(s): February 19, 1996
Received by editor(s) in revised form: October 25, 1996
Article copyright: © Copyright 1998 American Mathematical Society