In this paper, we propose a novel gradient recovery method for elliptic interface problem using body-fitted mesh in two dimension. Due to the lack of regularity of solution at interface, standard gradient recovery methods fail to give superconvergent results, and thus will lead to overrefinement when served as a posteriori error estimator. This drawback is overcome by designing an immersed gradient recovery operator in our method. We prove the superconvergence of this method for both mildly unstructured mesh and adaptive mesh, and present several numerical examples to verify the superconvergence and its robustness as a posteriori error estimator.

Hailong Guo

Xu Yang

Communications in Computational Physics

COMMUNICATIONS IN COMPUTATIONAL PHYSICS (CICP) 发表在物理问题的计算建模方面具有高科学价值的原创研究和调查论文。将展示所有物理科学中多物理和多尺度创新计算方法和建模的结果。

Communications in Computational Physics (CICP) publishes original research and survey papers of high scientific value in the field of computational modeling of physical problems. The journal showcases results of innovative computational methods and modeling across multiple physics disciplines, emphasizing multiphysics and multiscale approaches.

《Communications in Computational Physics》发表具有高科学价值的原创研究和调查论文，专注于物理问题的计算建模。期刊展示了在所有物理科学领域中，多物理和多尺度创新计算方法及建模的研究成果。

Gradient Recovery for Elliptic Interface Problem: I. Body-Fitted Mesh

The superconvergence of this gradient recovery method for elliptic interface problem using body-fitted mesh in two dimension is proved and its robustness as a posteriori error estimator is verified.

Category	Quartile
物理与天体物理	3
物理与天体物理, 物理数学物理	4

Gradient Recovery for Elliptic Interface Problem: I. Body-Fitted Mesh

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Journal Info

Category	Quartile
PHYSICS, MATHEMATICAL	1