Journal ArticleDOI
Coupling of the Crank–Nicolson scheme and localized meshless technique for viscoelastic wave model in fluid flow
O. Nikan,Zakieh Avazzadeh +1 more
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TLDR
An efficient localized meshless technique for approximating the viscoelastic wave model by decomposing the initial domain into several sub-domains and constructing a local radial basis function approximation over every sub-domain is proposed.About:
This article is published in Journal of Computational and Applied Mathematics.The article was published on 2021-12-15. It has received 30 citations till now. The article focuses on the topics: Basis function & Temporal discretization.read more
Citations
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Numerical approach for modeling fractional heat conduction in porous medium with the generalized Cattaneo model
TL;DR: In this paper, an accurate and robust meshless technique for approximating the solution of the time fractional Cattaneo model applied to the heat flow in a porous medium is proposed.
Journal ArticleDOI
An efficient local meshless method for the equal width equation in fluid mechanics
TL;DR: In this article, an accurate and robust meshless approach for the numerical solution of the nonlinear equal width equation is proposed, which is based on the localized radial basis function-finite difference (RBF-FD) method.
Journal ArticleDOI
Soliton solutions of the nonlinear sine-Gordon model with Neumann boundary conditions arising in crystal dislocation theory
TL;DR: In this article, an efficient and accurate localized meshless collocation method to find the approximate solution of the nonlinear sine-Gordon equation with Neumann boundary conditions in two space variables is proposed.
Journal ArticleDOI
Numerical treatment of microscale heat transfer processes arising in thin films of metals
TL;DR: In this article , a localized radial basis function partition of unity (LRBF-PU) method was proposed to find the MHTE solution in two phases: first, the discretization of time dimension is obtained through the finite difference with second order accuracy.
Journal ArticleDOI
An efficient localized meshless collocation method for the two-dimensional Burgers-type equation arising in fluid turbulent flows
TL;DR: In this paper , a local radial basis function partition of unity (LRBF-PU) method was proposed to approximate the spatial direction and a fully-discrete scheme was established.
References
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Book
Functional Analysis, Sobolev Spaces and Partial Differential Equations
TL;DR: In this article, the theory of conjugate convex functions is introduced, and the Hahn-Banach Theorem and the closed graph theorem are discussed, as well as the variations of boundary value problems in one dimension.
Journal ArticleDOI
The partition of unity finite element method: Basic theory and applications
Jens Markus Melenk,Ivo Babuška +1 more
TL;DR: In this article, the basic ideas and the mathematical foundation of the partition of unity finite element method (PUFEM) are presented and a detailed and illustrative analysis is given for a one-dimensional model problem.
Journal ArticleDOI
Piecewise polynomial, positive definite and compactly supported radial functions of minimal degree
TL;DR: A new class of positive definite and compactly supported radial functions which consist of a univariate polynomial within their support is constructed, it is proved that they are of minimal degree and unique up to a constant factor.
Journal ArticleDOI
The Partition of Unity Method
Ivo Babuška,Jens Markus Melenk +1 more
TL;DR: In this article, a new finite element method is presented that features the ability to include in the finite element space knowledge about the partial differential equation being solved, which can therefore be more efficient than the usual finite element methods.
Book
Radial Basis Functions: Theory and Implementations
TL;DR: In this paper, a radial basis function approximation on infinite grids is proposed, based on the wavelet method with radial basis functions (WBFF) with compact support, which is a general method for approximation and interpolation.
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