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

DOI:
https://doi.org/10.1090/S0025-5718-98-00946-6

MathSciNet review:
1459390

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Abstract | References | Similar Articles | Additional Information

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 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

Email:
ohannes@math.utk.edu

**Charalambos Makridakis**

Affiliation:
Department of Mathematics, University of Crete, 714 09 Heraklion, Crete, Greece

Email:
makr@sargos.math.uch.gr

DOI:
https://doi.org/10.1090/S0025-5718-98-00946-6

Received by editor(s):
February 19, 1996

Received by editor(s) in revised form:
October 25, 1996

Article copyright:
© Copyright 1998
American Mathematical Society