An adaptive finite element method for semilinear parabolic interface problems with nonzero flux jump - Ray, Tanushree; Sinha, Rajen Kumar (Applied numerical mathematics, 2020)
We present and analyze an adaptive finite element method for a semilinear parabolic interface problem subject to nonzero flux jump in a two-dimensional bounded convex polygonal domain. The residual-based a posteriori error estimates are derived using energy argument. Our strategy is to avoid solving the nonlinear system by considering a linearized fully discrete scheme. An adaptive algorithm is constructed using the derived error estimators. A global upper bound for the error is derived which is bounded by the element residual and interior jump residual, whereas a local lower bound in terms of the space error indicator is established. The theory presented is complemented by numerical experiments to illustrate the proposed algorithm.