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Natural neighbour Galerkin methods [PDF]
International Journal for Numerical Methods in Engineering, 2000 Natural neighbour co-ordinates (Sibson co-ordinates) is a well-known interpolation scheme for multivariate data fitting and smoothing. The numerical implementation of natural neighbour co-ordinates in a Galerkin method is known as the natural element method (NEM).
V. V. Belikov +3 more
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Numerical analysis of the neutron multigroup $SP_N$ equations
Comptes Rendus. Mathématique, 2021 The multigroup neutron $SP_N$ equations, which are an approximation of the neutron transport equation, are used to model nuclear reactor cores. In their steady state, these equations can be written as a source problem or an eigenvalue problem.
Jamelot, Erell, Madiot, François
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The Local Discontinuous Galerkin Method for Time-Dependent Convection-Diffusion Systems
, 1998 In this paper, we study the local discontinuous Galerkin (LDG) methods for nonlinear, time-dependent convection-diffusion systems. These methods are an extension of the Runge--Kutta discontinuous Galerkin (RKDG) methods for purely hyperbolic systems to ...
Bernardo Cockburn, Chi-Wang Shu
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Wavelet-Galerkin Quasilinearization Method for Nonlinear Boundary Value Problems
Abstract and Applied Analysis, 2014 A numerical method is proposed by wavelet-Galerkin and quasilinearization approach for nonlinear boundary value problems. Quasilinearization technique is applied to linearize the nonlinear differential equation and then wavelet-Galerkin method is ...
Umer Saeed, Mujeeb ur Rehman
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Interval element-free Galerkin method for uncertain mechanical problems
Advances in Mechanical Engineering, 2018 An interval element-free Galerkin method was proposed to solve some issues in structural design and analysis of structural parameters that have errors or uncertainties caused by manufacture, installation, measurement, or computation.
Li Ming Zhou, Erfei Zhao, Shuhui Ren
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On the generalized wavelet-Galerkin method [PDF]
Journal of Computational and Applied Mathematics, 2018 In the frame of the traditional wavelet-Galerkin method based on the compactly supported wavelets, it is important to calculate the so-called connection coefficients that are some integrals whose integrands involve products of wavelets, their derivatives as well as some known coefficients in considered differential equations.
Zhaochen Yang, Shijun Liao
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Numerical Solution of a Fractional Model for HIV Infection of CD4+T Cells via Legendre Multiwavelet Functions [PDF]
International Journal Bioautomation, 2020 In this paper, we introduce a Galerkin method based on Legendre multiwavelet functions to obtain approximate solutions of a fractional model for HIV infection of CD4+T cells corresponding to a class of systems of nonlinear fractional differential ...
Ensiyeh Sokhanvar +1 more
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A weighted Nitsche discontinuous Galerkin finite element method for plane problems
Journal of Hebei University of Science and Technology, 2018 The classical discontinuous Galerkin finite element method has the unstable numerical problem resulting from the inappropriate stability parameter for elasticity problem with interfaces.
Xiaowei DENG +2 more
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Research in the Mathematical Sciences, 2017 In this paper we study the stochastic Galerkin approximation for the linear transport equation with random inputs and diffusive scaling. We first establish uniform (in the Knudsen number) stability results in the random space for the transport equation ...
Shi Jin, Jian‐Guo Liu, Zheng Ma
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Mathematics of Computation, 2016 In this paper we consider the local discontinuous Galerkin method based on the generalized alternating numerical fluxes, for solving the linear convection-diffusion equations in one dimension and two dimensions.
Yao Cheng, Xiong Meng, Qiang Zhang
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