Abstract

AbstractIn this work, we discuss a posteriori error control and adaptivity in the setting of the finite cell method (FCM). For this purpose, we introduce k-times differentiable basis functions for hp-adaptive meshes consisting of paraxial rectangles with arbitrary-level hanging nodes suitable for the immersed-boundary setting of the FCM. Furthermore, we present error control for Poisson’s problem in the context of the finite cell method. To this end, we establish a reliable residual-based estimator for the energy error. Additionally, we introduce a dual-weighted residual estimator capable of separating the discretization error from the quadrature error which poses a second error source typically arising in the FCM. Several numerical experiments illustrate the reliability and efficiency properties of the estimators.

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