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

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- by Ohannes Karakashian and Charalambos Makridakis PDF
- Math. Comp.
**67**(1998), 479-499 Request permission

## 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.## References

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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
- MR Author ID: 289627
- Email: makr@sargos.math.uch.gr
- Received by editor(s): February 19, 1996
- Received by editor(s) in revised form: October 25, 1996
- © Copyright 1998 American Mathematical Society
- 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