Finite difference approximation of a parabolic problem with variable coefficients | Zendy

Boško S. Jovanović | Zendy; Zorica Milovanović Jeknić | Zendy

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Finite difference approximation of a parabolic problem with variable coefficients

Author(s) -

Boško S. Jovanović,

Zorica Milovanović Jeknić

Publication year - 2014

Publication title -

publications de l institut mathematique

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.246

H-Index - 17

eISSN - 1820-7405

pISSN - 0350-1302

DOI - 10.2298/pim1409049j

Subject(s) - mathematics , sobolev space , mathematical analysis , norm (philosophy) , logarithm , rate of convergence , variable (mathematics) , a priori and a posteriori , convergence (economics) , boundary value problem , parabolic partial differential equation , partial differential equation , channel (broadcasting) , philosophy , electrical engineering , epistemology , economic growth , political science , law , economics , engineering

We study the convergence of a finite difference scheme that approximates the third initial-boundary-value problem for a parabolic equation with variable coefficients on a unit square. We assume that the generalized solution of the problem belongs to the Sobolev space W s,s/2 2, s≤3. An almost second-order convergence rate estimate (with additional logarithmic factor) in the discrete W 1,1/2 2 norm is obtained. The result is based on some nonstandard a priori estimates involving fractional order discrete Sobolev norms. [Projekat Ministarstva nauke Republike Srbije, br. 174015]

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