Galerkin Method with Discontinuous Basis Functions on Staggered Grips a Priory Estimates for the Homogeneous Dirichlet Problem

We describe a Galerkin method with special basis functions for a class of singular two-point boundary value problems. The convergence is shown which is ofO(h2)for a certain subclass of the problems.

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Eigencurves of the p(·)-Biharmonic operator with a Hardy-type term

Moroccan Journal of Pure and Applied Analysis ◽

10.2478/mjpaa-2020-0015 ◽

2020 ◽

Vol 6 (2) ◽

pp. 198-209

Author(s):

Mohamed Laghzal ◽

Abdelouahed El Khalil ◽

My Driss Morchid Alaoui ◽

Abdelfattah Touzani

Keyword(s):

Dirichlet Problem ◽

Variational Approach ◽

Type Inequality ◽

Biharmonic Operator ◽

Nondecreasing Sequence ◽

Hardy Type Inequality ◽

Principal Curve ◽

Hardy Type ◽

Homogeneous Dirichlet Problem

AbstractThis paper is devoted to the study of the homogeneous Dirichlet problem for a singular nonlinear equation which involves the p(·)-biharmonic operator and a Hardy-type term that depend on the solution and with a parameter λ. By using a variational approach and min-max argument based on Ljusternik-Schnirelmann theory on C1-manifolds [13], we prove that the considered problem admits at least one nondecreasing sequence of positive eigencurves with a characterization of the principal curve μ1(λ) and also show that, the smallest curve μ1(λ) is positive for all 0 ≤ λ < CH, with CH is the optimal constant of Hardy type inequality.

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Efficiently convergent novel basis functions for the analysis of microstrip discontinuities by the spectral domain Galerkin method

annals of telecommunications - annales des télécommunications ◽

10.1007/bf02997624 ◽

1998 ◽

Vol 53 (1-2) ◽

pp. 23-27

Author(s):

Mohamed Essaaidi ◽

Jamal El Aoufi ◽

Ahmed El Moussaoui

Keyword(s):

Galerkin Method ◽

Basis Functions ◽

Spectral Domain ◽

Microstrip Discontinuities

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An Adaptive Approach to Solutions of Fredholm Integral Equations of the Second Kind

Abstract and Applied Analysis ◽

10.1155/2014/629179 ◽

2014 ◽

Vol 2014 ◽

pp. 1-13

Author(s):

Nebiye Korkmaz ◽

Zekeriya Güney

Keyword(s):

Galerkin Method ◽

Integral Equations ◽

Iteration Method ◽

Legendre Polynomials ◽

Optimization Problem ◽

Approximate Solutions ◽

Basis Functions ◽

Fredholm Integral Equations ◽

Coarse Mesh ◽

Fine Mesh

As an approach to approximate solutions of Fredholm integral equations of the second kind, adaptive hp-refinement is used firstly together with Galerkin method and with Sloan iteration method which is applied to Galerkin method solution. The linear hat functions and modified integrated Legendre polynomials are used as basis functions for the approximations. The most appropriate refinement is determined by an optimization problem given by Demkowicz, 2007. During the calculationsL2-projections of approximate solutions on four different meshes which could occur between coarse mesh and fine mesh are calculated. Depending on the error values, these procedures could be repeated consecutively or different meshes could be used in order to decrease the error values.

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