A modified L-scheme to solve nonlinear diffusion problems

K. Mitra (Corresponding author), I.S. Pop

Onderzoeksoutput: Bijdrage aan tijdschriftTijdschriftartikelAcademicpeer review

40 Citaten (Scopus)
2 Downloads (Pure)


In this work, we propose a linearization technique for solving nonlinear elliptic partial differential equations that are obtained from the time-discretization of a wide variety of nonlinear parabolic problems. The scheme is inspired by the L-scheme, which gives unconditional convergence of the linear iterations. Here we take advantage of the fact that at a particular time step, the initial guess for the iterations can be taken as the solution of the previous time step. First it is shown for quasilinear equations that have linear diffusivity that the scheme always converges, irrespective of the time step size, the spatial discretization and the degeneracy of the associated functions. Moreover, it is shown that the convergence is linear with convergence rate proportional to the time step size. Next, for the general case it is shown that the scheme converges linearly if the time step size is smaller than a certain threshold which does not depend on the mesh size, and the convergence rate is proportional to the square root of the time step size. Finally numerical results are presented that show that the scheme is at least as fast as the modified Picard scheme, faster than the L-scheme and is more stable than the Newton or the Picard scheme.

Originele taal-2Engels
Pagina's (van-tot)1722-1738
Aantal pagina's17
TijdschriftComputers and Mathematics with Applications
Nummer van het tijdschrift6
StatusGepubliceerd - 15 mrt. 2019


Duik in de onderzoeksthema's van 'A modified L-scheme to solve nonlinear diffusion problems'. Samen vormen ze een unieke vingerafdruk.

Citeer dit