Gradient WEB-spline finite element method for solving two-dimensional quasilinear elliptic problems

Zakeri, Ali; Shayegan, Amir Hossein Salehi

doi:10.1016/j.apm.2013.06.018

Cited by 4 publications

(2 citation statements)

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“…Having the above mentioned notations in mind, we can split the set of K indices into subsets: inner B-splines, I, and outer B-splines, J. In other words K = I ∪ J, see [6,11,13].…”

Section: Web-spline Basismentioning

confidence: 99%

“…Although this method is stable and convergent, but one should solve a large system of equations for each iteration. So, to deal with this difficulty, instead of FEM, WEB-spline finite element method was applied in [13]. The WEB-spline basis belongs to H 2 (Ω) ∩ H 1 0 (Ω), has been considered as test functions in FEM and consequently reduced the order of the system.…”

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confidence: 99%

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A Numerical Method for SolvingTwo-Dimensional Nonlinear Parabolic ProblemsBased on a Preconditioning Operator

Shayegan

Zakeri

Hosseini

2020

Mathematical Modelling and Analysis

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This article considers a nonlinear system of elliptic problems, which is obtained by discretizing the time variable of a two-dimensional nonlinear parabolic problem. Since the system consists of ill-conditioned problems, therefore a stabilized, mesh-free method is proposed. The method is based on coupling the preconditioned Sobolev space gradient method and WEB-spline finite element method with Helmholtz operator as a preconditioner. The convergence and error analysis of the method are given. Finally, a numerical example is solved by this preconditioner to show the efficiency and accuracy of the proposed methods.

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“…Having the above mentioned notations in mind, we can split the set of K indices into subsets: inner B-splines, I, and outer B-splines, J. In other words K = I ∪ J, see [6,11,13].…”

Section: Web-spline Basismentioning

confidence: 99%

mentioning

confidence: 99%