Abstract
In this paper, we consider the two-dimensional time-dependent Schrödinger equation. Firstly, we use the rectangular Lagrange type finite element of order p to get a semi-discrete scheme of the equation and discuss the superconvergence error estimate in the H1 norm. Secondly, we use the Crank–Nicolson method in time to get a fully discrete scheme of the equation, and the superconvergence estimate in the H1 norm can be obtained in this scheme. Finally, a numerical example with the order p=1 is provided to verify our theoretical results.
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Schedule a callMore From: Computers & mathematics with applications (Oxford, England : 1987)
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