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Akrivis, Georgios; Lubich, Christian

Fully implicit, linearly implicit and implicit-explicit backward difference formulae for quasi-linear parabolic equations. (English) Zbl 1334.65124

Numer. Math. 131, No. 4, 713-735 (2015).
The paper presents a study on the stability and convergence of tie discretizations of quasi-linear parabolic equations With the abstract setting of the problem and stating some preliminaries, the existence and uniqueness of the several approximations in Hilbert spaces are discussed. The authors establish optimal order a priori error bounds for the various difference schemes by energy estimates.
Reviewer: K. N. Shukla (Gurgaon)

Cited in 36 Documents

MSC:

65M06 Finite difference methods for initial value and initial-boundary value problems involving PDEs
65M12 Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs
35K59 Quasilinear parabolic equations
65M15 Error bounds for initial value and initial-boundary value problems involving PDEs

Keywords:

quasi-linear parabolic equations; implicit finite difference method; implicit-explicit backward difference scheme; consistency; stability; convergence; error bound

Software:

RODAS
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Full Text: DOI

References:

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