AnH1-Galerkin Mixed Finite Element Method for Parabolic Partial Differential Equations

Pani, Amiya K.

doi:10.1137/s0036142995280808

Cited by 96 publications

(50 citation statements)

References 23 publications

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“…On the other hand, H 1 -Galerkin mixed finite element method (see [4]) has been under rapid progress recently since this method has the following advantages over classical mixed finite element method. The method allows the approximation spaces to be polynomial spaces with different orders without LBB consistency condition and there is no requirement of the quasi-uniform assumption on the meshes.…”

Section: A Amentioning

confidence: 99%

“…The method allows the approximation spaces to be polynomial spaces with different orders without LBB consistency condition and there is no requirement of the quasi-uniform assumption on the meshes. For example, Pani [4,5] proposed an H 1 -Galerkin mixed finite element procedure to deal with parabolic partial differential equations and parabolic partial integro-differential equations, respectively. Liu and Li [6,7] applied this method to deal with pseudohyperbolic equations and fourth-order heavy damping wave equation.…”

Section: A Amentioning

confidence: 99%

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Nonconforming H1-Galerkin Mixed Finite Element Method for Pseudo-Hyperbolic Equations

Zhang¹,

Niu²,

Shi³

2012

AJCM

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Based on H 1 -Galerkin mixed finite element method with nonconforming quasi-Wilson element, a numerical approximate scheme is established for pseudo-hyperbolic equations under arbitrary quadrilateral meshes. The corresponding optimal order error estimate is derived by the interpolation technique instead of the generalized elliptic projection which is necessary for classical error estimates of finite element analysis.

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Section: A Amentioning

confidence: 99%

Section: A Amentioning

confidence: 99%

Nonconforming H1-Galerkin Mixed Finite Element Method for Pseudo-Hyperbolic Equations

Zhang¹,

Niu²,

Shi³

2012

AJCM

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“…The H 1 -mfem considered in this article is based on an approach suggested by Pani for nonlinear parabolic equations [3]. Pany et al [4] adapted the method to Burgers equation.…”

Section: Introductionmentioning

confidence: 99%

Estimating the error of a \(H^{1}\)-mixed finite element solution for the Burgers equation

Shafie

Tran

2016

ANZIAMJ

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We compute error estimations for a H 1 -mixed finite element method for Burgers equation. By using a H 1 -mixed finite element method, the problem is reformulated as a system of first order partial differential equations, which allows an approximation of the unknown function and its derivative. Local parabolic and elliptic methods approximate the true errors from the computed solutions; the so-called a posteriori error estimates. Numerical experiments show that the error estimations converge to the true errors.

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“…Pani [6] (in 1998) proposed the H 1 MFEM of the linear parabolic equation. Compared to standard mixed methods, the proposed method has several attractive features.…”

Section: Introductionmentioning

confidence: 99%

Numerical Analysis of A Mixed Finite Element Method for Rosenau-Burgers Equation

Wang¹

2015

Proceedings of the 2015 International Industrial Informatics and Computer Engineering Conference

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Abstract. An H 1 -Galerkin mixed finite element method (H 1 MFEM) is proposed and analyzed for the fourth-order nonlinear Rosenau-Burgers equation. By introducing three auxiliary variables, the first-order system of four equations is formulated. The fully discrete scheme is studied for problem and optimal a priori error estimates for L 2 and H 1 -norms for the scalar unknown, first derivative, second derivative and third derivative are obtained simultaneously.

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AnH¹-Galerkin Mixed Finite Element Method for Parabolic Partial Differential Equations

Cited by 96 publications

References 23 publications

Nonconforming <i>H</i><sup>1</sup>-Galerkin Mixed Finite Element Method for Pseudo-Hyperbolic Equations

Nonconforming <i>H</i><sup>1</sup>-Galerkin Mixed Finite Element Method for Pseudo-Hyperbolic Equations

Estimating the error of a \(H^{1}\)-mixed finite element solution for the Burgers equation

Numerical Analysis of A Mixed Finite Element Method for Rosenau-Burgers Equation

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AnH1-Galerkin Mixed Finite Element Method for Parabolic Partial Differential Equations

Cited by 96 publications

References 23 publications

Nonconforming &lt;i&gt;H&lt;/i&gt;&lt;sup&gt;1&lt;/sup&gt;-Galerkin Mixed Finite Element Method for Pseudo-Hyperbolic Equations

Nonconforming &lt;i&gt;H&lt;/i&gt;&lt;sup&gt;1&lt;/sup&gt;-Galerkin Mixed Finite Element Method for Pseudo-Hyperbolic Equations

Estimating the error of a \(H^{1}\)-mixed finite element solution for the Burgers equation

Numerical Analysis of A Mixed Finite Element Method for Rosenau-Burgers Equation

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Product

Resources

About

AnH¹-Galerkin Mixed Finite Element Method for Parabolic Partial Differential Equations

Nonconforming <i>H</i><sup>1</sup>-Galerkin Mixed Finite Element Method for Pseudo-Hyperbolic Equations

Nonconforming <i>H</i><sup>1</sup>-Galerkin Mixed Finite Element Method for Pseudo-Hyperbolic Equations