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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

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  • 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 supported 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

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@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 supported 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, biharmonic, Poisson, 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 supported 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 and Z. Zhang. (2008). 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:
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