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.
ADEWOLE, MATTHEW OLAYIWOLA and PAYNE, VICTOR FOLARIN
"Linearized four-step implicit scheme for nonlinear parabolic interface problems,"
Turkish Journal of Mathematics: Vol. 42:
6, Article 17.
Available at: https://journals.tubitak.gov.tr/math/vol42/iss6/17