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The Runge-Kutta Discontinuous Galerkin Method for Conservation Laws V
, 1998This is the fifth paper in a series in which we construct and study the so-called Runge?Kutta discontinuous Galerkin method for numerically solving hyperbolic conservation laws. In this paper, we extend the method to multidimensional nonlinear systems of
Bernardo Cockburn, Chi-Wang Shu
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Galerkin's method and stability
Mathematical Methods in the Applied Sciences, 1980AbstractApproximation in least squares by Galerkin's method leads to a consideration of strongly minimal systems. Theorems are derived which permit the recognition of systems which are not strongly minimal from the characteristics of the elements themselves.
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Function generation by Galerkin's method
Mechanism and Machine Theory, 1989Abstract An original method referred to as Galerkin's method in mathematics has been proposed for determining the dimensions of a mechanism which is to approximate a given continuous function. The application of this method has been shown on a four-bar for 3- and 5-parameter cases.
AKCALI, ID, DITTRICH, G
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A scalable galerkin multigrid method for real-time simulation of deformable objects
ACM Transactions on Graphics, 2019We propose a simple yet efficient multigrid scheme to simulate high-resolution deformable objects in their full spaces at interactive frame rates. The point of departure of our method is the Galerkin projection which is simple to construct.
Zangyueyang Xian, Xin Tong, Tiantian Liu
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, 2016
Using the interpolating moving least-squares (IMLS) method to form the shape function, a novel improved element-free Galerkin (IEFG) method is presented for solving nonlinear elastic large deformation problems.
Yumin Cheng +3 more
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Using the interpolating moving least-squares (IMLS) method to form the shape function, a novel improved element-free Galerkin (IEFG) method is presented for solving nonlinear elastic large deformation problems.
Yumin Cheng +3 more
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SIAM Journal on Numerical Analysis, 2018
In this article, a new weak Galerkin finite element method is introduced to solve convection-diffusion--reaction equations in the convection dominated regime.
R. Lin, X. Ye, Shangyou Zhang, P. Zhu
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In this article, a new weak Galerkin finite element method is introduced to solve convection-diffusion--reaction equations in the convection dominated regime.
R. Lin, X. Ye, Shangyou Zhang, P. Zhu
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Discontinuous Galerkin Methods [PDF]
, 2012 In this final chapter we present the discontinuous Galerkin (dG) method. This method is based on finite element spaces that consist of discontinuous piecewise polynomials defined on a partition of the computational domain. Such methods are very flexible, for example, since they allow construction of more general methods and since they allow for simple ...
Mats G. Larson, Fredrik Bengzon
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The Standard Galerkin Method [PDF]
, 1997 In this introductory chapter we shall study the standard Galerkin finite element method for the approximate solution of the model initial-boundary value problem for the heat equation, $$\eqalign{ & u_t - \Delta u = f{\text{ }}in\:{\text{ }}\Omega ,\:{\text{ }}for\:t > 0, \cr & u = 0\:on\:\partial \Omega ,\:for\:t > 0,\:with\:u(\cdot,0) = v\:in ...
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The Interpolating Complex Variable Element-Free Galerkin Method for Temperature Field Problems
, 2015In this paper, an interpolating complex variable moving least-squares (ICVMLS) method is presented. In the ICVMLS method, the trial function of a two-dimensional problem is formed with a one-dimensional basis function, and the shape function of the ...
Yajie Deng +3 more
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1977
Consider a separable Hilbert space H and a set M of its elements which is dense in H. According to Theorem 6.18, p. 79, if for some element u ∈ H $$\left( {u,v} \right) = 0\,\,\,holds\,for\,every\,\,\,v \in M,$$ (14.1) then it follows that u = 0 in H. Let now $${\varphi _1},{\varphi _2},\,...$$ (14.2) be a base in H. The assertion is
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Consider a separable Hilbert space H and a set M of its elements which is dense in H. According to Theorem 6.18, p. 79, if for some element u ∈ H $$\left( {u,v} \right) = 0\,\,\,holds\,for\,every\,\,\,v \in M,$$ (14.1) then it follows that u = 0 in H. Let now $${\varphi _1},{\varphi _2},\,...$$ (14.2) be a base in H. The assertion is
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