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An adaptive high-order unfitted finite element method for elliptic interface problems (2009.01656v3)
Published 3 Sep 2020 in math.NA and cs.NA
Abstract: We design an adaptive unfitted finite element method on the Cartesian mesh with hanging nodes. We derive an hp-reliable and efficient residual type a posteriori error estimate on K-meshes. A key ingredient is a novel hp-domain inverse estimate which allows us to prove the stability of the finite element method under practical interface resolving mesh conditions and also prove the lower bound of the hp a posteriori error estimate. Numerical examples are included.