The Method of Lines With a Finite Volumes Approach for Transient Convection-Diffusion Problems

Ondami, Bienvenu

doi:10.18642/jmsaa_7100121779

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2018

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“…Proof. The proof is identical to that given in [13]. We write the scheme (19) in the following form for the inner points:…”

Section: Explicit Schemementioning

confidence: 98%

Finite volume discretization of a class of parabolic equations with discontinuous and oscillating coefficients

Ondami¹

2018

ams

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In this paper we consider the numerical approximation of a class of parabolic equations with highly oscillating and discontinuous coefficients. We use the method of lines with a finite volumes approach to discretize this problem. This discretization leads to an ordinary differential equation (ODE). We then analyze two families of numerical schemes corresponding to explicit and implicit discretization of the obtained ODE. Numerical results comparing the approximation obtained by this method and the homogenized problem's solution are presented. They show that this method is accurate and robust for the class of problems studied.Mathematics Subject Classification: 65M08, 65M20

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“…Proof. The proof is identical to that given in [13]. We write the scheme (19) in the following form for the inner points:…”

Section: Explicit Schemementioning

confidence: 98%

Finite volume discretization of a class of parabolic equations with discontinuous and oscillating coefficients

Ondami¹

2018

ams

Self Cite

View full text Add to dashboard Cite

show abstract

The Method of Lines With a Finite Volumes Approach for Transient Convection-Diffusion Problems

Cited by 1 publication

References 10 publications

Finite volume discretization of a class of parabolic equations with discontinuous and oscillating coefficients

Finite volume discretization of a class of parabolic equations with discontinuous and oscillating coefficients

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