Abstract
We prove a posteriori error estimates of optimal order for linear Schrodinger-type equations in the L8(L(2)- and the L8(H1)-norm. We discretize only in time by the Crank-Nicolson method. The direct use of the reconstruction technique, as it has been proposed by Akrivis et al. in [Math. Comput. 75 (2006) 511-531], leads to a posteriori upper bounds that are of optimal order in the L8(L2)-norm, but of suboptimal order in the L8(H(1)-norm. The optimality in the case of L8(H(1))-norm is recovered by using an auxiliary initial-and boundary-value problem.
Original language | English |
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Pages (from-to) | 761-778 |
Number of pages | 18 |
Journal | Esaim: Mathematical Modelling and Numerical Analysis |
Volume | 45 |
Issue number | 4 |
Early online date | 21 Feb 2011 |
DOIs | |
Publication status | Published - Jul 2011 |
Keywords
- TIME
- energy techniques
- GALERKIN METHOD
- a posteriori error analysis
- Crank-Nicolson method
- Linear Schrodinger equation
- FINITE-ELEMENT-METHOD
- L(infinity)(L(2))- and L(infinity)(H(1))-norm
- Crank-Nicolson reconstruction