An efficient Legendre-Galerkin approximation for the fourth-order equation with singular potential and SSP boundary condition

Abstract: In this article, we develop an efficient Legendre-Galerkin approximation based on a reduced-dimension scheme for the fourth-order equation with singular potential and simply supported plate (SSP) boundary conditions in a circular domain. First, we deduce the equivalent reduced-dimension scheme and essential pole condition associated with the original problem, based on which a class of weighted Sobolev spaces are defined and a weak formulation and its discrete scheme are also established for each reduced one-dimensional problem. Second, the existence and uniqueness of the weak solution and the approximation solutions are given using the Lax-Milgram theorem. Then, we construct a class of projection operators, give their approximation properties, and then prove the error estimates of the approximation solutions. In addition, we construct a set of effective basis functions in approximate space using orthogonal property of Legendre polynomials and derive the equivalent matrix form of the discrete scheme. Finally, a large number of numerical examples are performed, and the numerical results illustrate the validity and high accuracy of our algorithm.

Object Details

• Location: Deutsche Nationalbibliothek Frankfurt am Main
• Extent: Online-Ressource
• Language: Englisch

References and Relationships

• Bibliographic citation: An efficient Legendre-Galerkin approximation for the fourth-order equation with singular potential and SSP boundary condition ; volume:21 ; number:1 ; year:2023 ; extent:16 ; Open mathematics ; 21, Heft 1 (2023) (gesamt 16)

Contributors, Places and Time

• Creator: Zou, Shuimu ; Zhang, Jun

Further information

• DOI: 10.1515/math-2023-0128
• URN: urn:nbn:de:101:1-2023122213284423880648
• Rights: Open Access; Der Zugriff auf das Objekt ist unbeschränkt möglich.
• Last update: 15.08.2025, 7:25 AM CEST