Volume 5, Issue 1
Invalidity of Decoupling a Biharmonic Equation to Two Poisson Equations on Non-convex Polygons

S. Zhang & Z. Zhang

Int. J. Numer. Anal. Mod., 5 (2008), pp. 73-76

Published online: 2008-05

Preview Full PDF 568 2266
Export citation
  • Abstract

We clarify the validity of a method that decouples a boundary value problem of biharmonic equation to two Poisson equations on polygonal domains. The method provides a way of computing deflections of simply supportecl polygonal plates by using Poisson solvers. We show that such decoupling is not valid if the polygonal domain is not convex. It may fail even when the right hand side function is infinitely smooth and supported away from the reentrant corners.

  • Keywords

simply supported plate biharmonic Poisson decoupling

  • AMS Subject Headings

35J05 35J35 65N30

  • Copyright

COPYRIGHT: © Global Science Press

  • Email address
  • BibTex
  • RIS
  • TXT
@Article{IJNAM-5-73, author = {S. Zhang and Z. Zhang}, title = {Invalidity of Decoupling a Biharmonic Equation to Two Poisson Equations on Non-convex Polygons}, journal = {International Journal of Numerical Analysis and Modeling}, year = {2008}, volume = {5}, number = {1}, pages = {73--76}, abstract = {We clarify the validity of a method that decouples a boundary value problem of biharmonic equation to two Poisson equations on polygonal domains. The method provides a way of computing deflections of simply supportecl polygonal plates by using Poisson solvers. We show that such decoupling is not valid if the polygonal domain is not convex. It may fail even when the right hand side function is infinitely smooth and supported away from the reentrant corners. }, issn = {2617-8710}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/ijnam/798.html} }
TY - JOUR T1 - Invalidity of Decoupling a Biharmonic Equation to Two Poisson Equations on Non-convex Polygons AU - S. Zhang & Z. Zhang JO - International Journal of Numerical Analysis and Modeling VL - 1 SP - 73 EP - 76 PY - 2008 DA - 2008/05 SN - 5 DO - http://doi.org/ UR - https://global-sci.org/intro/article_detail/ijnam/798.html KW - simply supported plate KW - biharmonic KW - Poisson KW - decoupling AB - We clarify the validity of a method that decouples a boundary value problem of biharmonic equation to two Poisson equations on polygonal domains. The method provides a way of computing deflections of simply supportecl polygonal plates by using Poisson solvers. We show that such decoupling is not valid if the polygonal domain is not convex. It may fail even when the right hand side function is infinitely smooth and supported away from the reentrant corners.
S. Zhang & Z. Zhang. (1970). Invalidity of Decoupling a Biharmonic Equation to Two Poisson Equations on Non-convex Polygons. International Journal of Numerical Analysis and Modeling. 5 (1). 73-76. doi:
Copy to clipboard
The citation has been copied to your clipboard