Refined error estimates for Green kernel-based interpolation

Mohebalizadeh, Hamed; Fasshauer, Gregory E.; Adibi, Hojatollah

doi:10.1016/j.aml.2022.108258

Cited by 3 publications

(1 citation statement)

References 7 publications

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“…If we consider below that when

m

and

n

are different fractional variables, we can further get the absolute error estimate of the solution of the equation based on the theoretical knowledge of interpolation space described in [37].…”

Section: Convergent Analysis and Mathematics Samplementioning

confidence: 99%

Dynamic analysis of viscoelastic foundation plate with fractional Kelvin–Voigt model using shifted Bernstein polynomials

Qu,

Zhang,

Cui

et al. 2023

Math Methods in App Sciences

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The fractional Kelvin–Voigt (FKV) viscoelastic constitutive model has been employed to build the fractional differential governing equation of viscoelastic foundation plate. Shifted Bernstein polynomial algorithm is implemented to solve the governing equations on a direct time domain numerically. Furthermore, the validity of the method is demonstrated by convergent analysis and error estimation of a math example. Finally, the dynamic analysis of viscoelastic foundation plate under different uniform loads. The movement of plate with different aspect ratios in viscoelastic foundation under the same load is studied. The stress of viscoelastic foundation plates of two materials under identical loading situations is investigated.

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“…If we consider below that when

m

and

n

are different fractional variables, we can further get the absolute error estimate of the solution of the equation based on the theoretical knowledge of interpolation space described in [37].…”

Section: Convergent Analysis and Mathematics Samplementioning

confidence: 99%

Dynamic analysis of viscoelastic foundation plate with fractional Kelvin–Voigt model using shifted Bernstein polynomials

Qu,

Zhang,

Cui

et al. 2023

Math Methods in App Sciences

View full text Add to dashboard Cite

show abstract

Well-posedness of space fractional Ginzburg–Landau equations involving the fractional Laplacian arising in a Bose–Einstein condensation and its kernel based approximation

Mohebalizadeh

Adibi

Dehghan

2023

Communications in Nonlinear Science and Numerical Simulation

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Reproducing kernels of Sobolev–Slobodeckij˘ spaces via Green’s kernel approach: Theory and applications

Mohebalizadeh¹,

Fasshauer²,

Adibi³

2023

Anal. Appl.

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This paper extends the work of Fasshauer and Ye [Reproducing kernels of Sobolev spaces via a Green kernel approach with differential operators and boundary operators, Adv. Comput. Math. 38(4) (2011) 891921] in two different ways, namely, new kernels and associated native spaces are identified as crucial Hilbert spaces in applied mathematics. These spaces include the following spaces defined in bounded domains [Formula: see text] with smooth boundary: homogeneous Sobolev–Slobodeckij̆ spaces, denoted by [Formula: see text], and Sobolev–Slobodeckij̆ spaces, denoted by [Formula: see text], where [Formula: see text]. Our goal is accomplished by obtaining the Green’s solutions of equations involving the fractional Laplacian and fractional differential operators defined through interpolation theory. We provide a proof that the Green’s kernels satisfying these problems are symmetric and positive definite reproducing kernels of [Formula: see text] and [Formula: see text], respectively. Constructing kernels in these two ways enables the characterization of functions in native spaces based on their regularity. The Galerkin/collocation method, based on these kernels, is employed to solve various fractional problems, offering explicit or simplified calculations and efficient solutions. This method yields improved results with reduced computational costs, making it suitable for complex domains.

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Refined error estimates for Green kernel-based interpolation

Cited by 3 publications

References 7 publications

Dynamic analysis of viscoelastic foundation plate with fractional Kelvin–Voigt model using shifted Bernstein polynomials

Dynamic analysis of viscoelastic foundation plate with fractional Kelvin–Voigt model using shifted Bernstein polynomials

Well-posedness of space fractional Ginzburg–Landau equations involving the fractional Laplacian arising in a Bose–Einstein condensation and its kernel based approximation

Reproducing kernels of Sobolev–Slobodeckij˘ spaces via Green’s kernel approach: Theory and applications

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