An adaptive finite element method for semilinear parabolic interface problems with nonzero flux jump

• Published in: Applied numerical mathematics Vol. 153; pp. 381 - 398
• Main Authors: Ray, Tanushree, Sinha, Rajen Kumar
• Format: Journal Article
• Language: English
• Published: Elsevier B.V 01.07.2020
• Subjects: A posteriori error estimates; Adaptive algorithm; Parabolic interface problem; Semilinear; A posteriori error estimates; Adaptive algorithm; Parabolic interface problem; Semilinear
• ISSN: 0168-9274; 1873-5460
• DOI: 10.1016/j.apnum.2020.03.001

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.