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<p>We will consider the use of mixed finite element method for the semi-discretization of the Schrödinger integro-differential systems. We investigate the problem of boundary observability for the semi-discrete models. We show that the semi-discretization based on a mixed finite element method with two different basis functions for the position and its differentiation with respect to time of Schrödinger type integro-differential equation, are uniformly observability as the discretization parameter <i>h</i> goes to zero. Some numerical results are given to illustrate our theoretical finds.</p>

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Observability Inequalities of a Semi-discrete Schrödinger Integro-Differential Equation Derived from a Mixed Finite Element Method

  • 期刊论文

  • 发表日期：

    2025年8月4日

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  • Da Xu

摘要

We will consider the use of mixed finite element method for the semi-discretization of the Schrödinger integro-differential systems. We investigate the problem of boundary observability for the semi-discrete models. We show that the semi-discretization based on a mixed finite element method with two different basis functions for the position and its differentiation with respect to time of Schrödinger type integro-differential equation, are uniformly observability as the discretization parameter h goes to zero. Some numerical results are given to illustrate our theoretical finds.