Linearized four-step implicit scheme for nonlinear parabolic interface problems

Authors: MATTHEW OLAYIWOLA ADEWOLE, VICTOR FOLARIN PAYNE

Abstract: We present the solution of a second-order nonlinear parabolic interface problem on a quasiuniform triangular finite element with a linearized four-step implicit scheme used for the time discretization. The convergence of the scheme in $L^2$-norm is established under certain regularity assumptions using interpolation and elliptic projection operators. A numerical experiment is presented to support the theoretical result. It is assumed that the interface cannot be fitted exactly.

Keywords: Four-step implicit, interface, almost-optimal, nonlinear parabolic equation

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