Mixed covolume method for parabolic problems on triangular grids

Yang, Shuzhen; Jiang, Ziwen

doi:10.1016/j.amc.2009.06.068

Cited by 10 publications

(10 citation statements)

References 13 publications

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“…Ref. [21] The symmetry relation holds, and there exist positive constants C ,μ 1 independent of h such that …”

Section: Some Lemmasmentioning

confidence: 99%

Toward understanding the development of scleral ossicles in the chicken, Gallus gallus

Franz‐Odendaal

2008

Developmental Dynamics

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Scleral ossicles are dermal bones that are present in the eye of many vertebrates. Despite this, little is understood about their development. This study investigates the cellular dynamics during and after induction, and attempts to identify inducing factors. Both cell death and proliferation were found to play limited roles in mesenchymal condensation formation, but are involved in development of the inducing epithelium overlying the presumptive ossicle. Real-time reverse transcriptase polymerase chain reaction of candidate genes identified significant increases in sonic hedgehog (SHH) expression. In situ hybridization confirmed that SHH is exclusively expressed in the conjunctival (scleral) papillae and not in the mesenchyme. Direct localized inhibition of Hedgehog signaling, by means of cyclopamine, supports the finding that SHH may play a role in scleral ossicle induction. In addition, a nonfluctuating asymmetry with respect to the number of ossicles per eye was found. This study provides significant insight into understanding the development of the neural crest derived dermal bones. Developmental Dynamics 237: 3240 -3251, 2008.

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“…Ref. [21] The symmetry relation holds, and there exist positive constants C ,μ 1 independent of h such that …”

Section: Some Lemmasmentioning

confidence: 99%

Toward understanding the development of scleral ossicles in the chicken, Gallus gallus

Franz‐Odendaal

2008

Developmental Dynamics

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“…Ref. [21] The symmetry relation holds, and there exist positive constants C ,μ 2 independent of h such that …”

Section: Some Lemmasmentioning

confidence: 99%

“…Using the Raviart‐Thomas projection, similar to the proof in Refs. [21] and [26], we can get the fact that there exists an unique solution for the system (3.4).…”

Section: Some Lemmasmentioning

confidence: 99%

“…This article proposes a new numerical scheme to solve the two‐dimensional Sobolev equation with convection term by using expanded mixed covolume method. This method combines expanded mixed finite element [14, 15] and mixed covolume methods [16, 17, 18, 19, 20, 21, 22], not only can simultaneously compute more different physical quantities but also preserves the simplicity of finite volume method and maintains the mass conservation law, which is very important to fluid computations. Rui and Lu [23] proposed expanded mixed covolume scheme to solve the self‐adjoint elliptic problem based on rectangular grids and gave some numerical examples.…”

Section: Introductionmentioning

confidence: 99%

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An expanded mixed covolume method for sobolev equation with convection term on triangular grids

Fang

2012

Numerical Methods Partial

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The expanded mixed covolume method for the two-dimensional Sobolev equation with convection term is developed and studied. This method uses the lowest-order Raviart-Thomas mixed finite element space as the trial function space. By introducing a transfer operator γ h which maps the trial function space into the test function space and combining expanded mixed finite element with mixed covolume method, the continuousin-time, discrete-in-time expanded mixed covolume schemes are constructed, and optimal error estimates for these schemes are obtained. Numerical results are given to examine the validity and effectiveness of the proposed schemes.

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“…This method not only preserves the simplicity of finite difference and the high accuracy of finite element but maintains the mass conservation law, which is very important to fluid and under-ground fluid computations. The optimal convergence of the mixed covolume method for linear elliptic problems on triangular grids was given by Chou et al([4]), and Yang et al( [15]) extended this numerical method to the parabolic problem. In a mixed covolume method for differential systems (1.2) one uses two staggered irregular gridsa primal grid consisting of primal volumes (elements) and a dual grid consisting of covolumes (dual elements).…”

Section: Introductionmentioning

confidence: 99%

A Mixed Covolume Method For The Pseudo-Parabolic Integro-Differential Equation On Triangular Grids

Zhang¹,

Jiang²

2015

Advances in Computer Science Research

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Mixed covolume method for parabolic problems on triangular grids

Cited by 10 publications

References 13 publications

Toward understanding the development of scleral ossicles in the chicken, Gallus gallus

Toward understanding the development of scleral ossicles in the chicken, Gallus gallus

An expanded mixed covolume method for sobolev equation with convection term on triangular grids

A Mixed Covolume Method For The Pseudo-Parabolic Integro-Differential Equation On Triangular Grids

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