A Posteriori Error Analysis of Two-Step Backward Differentiation Formula Finite Element Approximation for Parabolic Interface Problems

摘要: This paper studies a residual-based posteriori error estimates for linear parabolic interface problems in bounded convex polygonal domain $$\mathbb {R}^2$$R2. We use the standard finite element spaces space which are allowed to change time and two-step backward differentiation formula (BDF-2) approximation at equidistant step is used discretizations. The essential ingredients analysis continuous piecewise quadratic space---time BDF-2 reconstruction Scott---Zhang interpolation estimates. Optimal order an almost optimal derived $$L^{\infty }(L^{2})$$Lź(L2)-norm using only energy method. interfaces assumed be of arbitrary shape but smooth our purpose. Numerical experiments performed validate asymptotic behaviour estimators.