Volume 30, Issue 1
An Effective Indirect Trefftz Method for Solving Poisson Equation in 2D

Caixia You & Guangde Zhang

J. Part. Diff. Eq., 30 (2017), pp. 1-10.

Published online: 2017-03

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  • Abstract

In the solution domain, the inhomogeneous part of Poisson equation is approximated with the 5-order polynomial using Galerkin method, and the particular solution of the polynomial can be determined easily. Then, the solution of the Poisson equation is approximated by superposition of the particular solution and the Tcomplete functions related to the Laplace equation. Unknown parameters are determined by Galerkinmethod, so that the approximate solution is to satisfy the boundary conditions. Comparison with analogous results of others numerical method, the two calculating examples of the paper indicate that the accuracy of themethod is very high, which also has a very fast convergence rate.

  • Keywords

Poisson equation indirect Trefftz method Galerkin method boundary problem numerical method

  • AMS Subject Headings

35A25

  • Copyright

COPYRIGHT: © Global Science Press

  • Email address

28978556@qq.com (Caixia You)

gd-zhang@wust.edu.cn (Guangde Zhang)

  • BibTex
  • RIS
  • TXT
@Article{JPDE-30-1, author = {You , Caixia and Zhang , Guangde }, title = {An Effective Indirect Trefftz Method for Solving Poisson Equation in 2D}, journal = {Journal of Partial Differential Equations}, year = {2017}, volume = {30}, number = {1}, pages = {1--10}, abstract = { In the solution domain, the inhomogeneous part of Poisson equation is approximated with the 5-order polynomial using Galerkin method, and the particular solution of the polynomial can be determined easily. Then, the solution of the Poisson equation is approximated by superposition of the particular solution and the Tcomplete functions related to the Laplace equation. Unknown parameters are determined by Galerkinmethod, so that the approximate solution is to satisfy the boundary conditions. Comparison with analogous results of others numerical method, the two calculating examples of the paper indicate that the accuracy of themethod is very high, which also has a very fast convergence rate.}, issn = {2079-732X}, doi = {https://doi.org/10.4208/jpde.v30.n1.1}, url = {http://global-sci.org/intro/article_detail/jpde/5067.html} }
TY - JOUR T1 - An Effective Indirect Trefftz Method for Solving Poisson Equation in 2D AU - You , Caixia AU - Zhang , Guangde JO - Journal of Partial Differential Equations VL - 1 SP - 1 EP - 10 PY - 2017 DA - 2017/03 SN - 30 DO - http://doi.org/10.4208/jpde.v30.n1.1 UR - https://global-sci.org/intro/article_detail/jpde/5067.html KW - Poisson equation KW - indirect Trefftz method KW - Galerkin method KW - boundary problem KW - numerical method AB - In the solution domain, the inhomogeneous part of Poisson equation is approximated with the 5-order polynomial using Galerkin method, and the particular solution of the polynomial can be determined easily. Then, the solution of the Poisson equation is approximated by superposition of the particular solution and the Tcomplete functions related to the Laplace equation. Unknown parameters are determined by Galerkinmethod, so that the approximate solution is to satisfy the boundary conditions. Comparison with analogous results of others numerical method, the two calculating examples of the paper indicate that the accuracy of themethod is very high, which also has a very fast convergence rate.
Caixia You & Guangde Zhang. (2019). An Effective Indirect Trefftz Method for Solving Poisson Equation in 2D. Journal of Partial Differential Equations. 30 (1). 1-10. doi:10.4208/jpde.v30.n1.1
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