GALERKIN METHODS FOR A SCHRODINGER-TYPE EQUATION WITH A DYNAMICAL BOUNDARY CONDITION IN TWO DIMENSIONS

被引：1

作者：

Antonopoulou, D. C. ^{[1
]}

机构：

[1] Univ Chester, Dept Math, Chester CH2 4NU, Cheshire, England

来源：

ESAIM-MATHEMATICAL MODELLING AND NUMERICAL ANALYSIS-MODELISATION MATHEMATIQUE ET ANALYSE NUMERIQUE | 2015年 / 49卷 / 04期

关键词：

2-D Schrodinger equation; finite element methods; error estimates; noncylindrical domain; Neumann boundary condition; cubic splines; Crank Nicolson time stepping; dynamical boundary condition; underwater acoustics; PARABOLIC EQUATION;

D O I：

10.1051/m2an/2015004

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper, we consider a two-dimensional Schrodinger-type equation with a dynamical boundary condition. This model describes the long-range sound propagation in naval environments of variable rigid bottom topography. Our choice for a regular enough finite element approximation is motivated by the dynamical condition and therefore, consists of a cubic splines implicit Galerkin method in space. Furthermore, we apply a Crank-Nicolson time stepping for the evolutionary variable. We prove existence and stability of the semidiscrete and fully discrete solution. Due to the complexity of the analyzed problem, we use very refined technics in order to derive estimates of the numerical error in the H-1-norm.

引用

页码：1127 / 1156

页数：30

共 19 条

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