A Collocation Spectral Element Method for Solving Boundary Value Problems of Elliptic Partial Differential Equations

Liping Wu, Hui Zhang, Chunping Pang

Abstract


In this paper, the collocation spectral element method is used to solve the boundary value problems of elliptic partial differential equations. In this method, the domain of definition is decomposed into several connected sub-domains by using the idea of finite element method, and then the elliptic partial differential equation is discretized by using the method of collocation spectrum on each sub-domain. Finally, the element rigid matrix is assembled into the total rigid matrix by using the idea of finite element method, and finally the boundary value problem of elliptic partial differential equation is obtained Numerical solution of unknown function. This method can be used to deal with the boundary value problems of some complex elliptic partial differential equations with variable coefficients, and can also find the numerical solutions of the boundary value problems of elliptic partial differential equations defined in the complex region. It can also simplify the programming and obtain the numerical solution with high precision. This is undoubtedly a great application value of this method.

Keywords


collocation spectral element method, boundary value problem of elliptic partial differential equation, numerical solution


DOI
10.12783/dtetr/mcaee2020/34992

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