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A weighted Nitsche’s method for interface problems with higher-order simplex elements

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Abstract

We develop a numerical strategy based on a weighted Nitsche’s approach to model a general class of interface problems with higher-order simplex elements. We focus attention on problems in which the jump in the field quantities across an interface is given. The presented method generalizes the weighted Nitsche’s approach of Annavarapu et al. (Comput. Meth. Appl. Mech. Eng. 225–228:44–54, 2012) to higher-order simplices. Specifically, for higher-order simplex elements, we derive closed-form analytical expressions for the stabilization parameter arising in Nitsche’s variational form. We also prescribe corresponding weights for the discrete fluxes in the consistency terms present in Nitsche’s variational form. The prescribed choice of weights is shown to be optimal such that it minimizes the stabilization parameter while ensuring coercivity of the bilinear form. In the presence of large contrasts in material properties and mesh sizes, the proposed weighting yields better conditioned systems than the traditional Nitsche formulation by bounding the maximum eigenvalue of the discrete system from above. Further, the geometrical representation of curved interfaces is improved through a hierarchical local renement approach. Several numerical examples are presented with quadratic triangles to demonstrate the efficacy of the presented method.

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Acknowledgements

Chandrasekhar Annavarapu gratefully acknowledges the support received from the Ministry of Human Resource Development and IIT Madras, under the grant SB20210856CEMHRD008957 to the Subsurface Mechanics and Geo-Energy Laboratory.

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Authors and Affiliations

  1. Computational Mechanics and Materials, Idaho National Laboratory, P.O. Box 1625, Idaho Falls, ID, 83415–3840, USA

    Wen Jiang

  2. Department of Civil and Environmental Engineering, Duke University, Durham, NC, 27708, USA

    Yingjie Liu

  3. Department of Civil Engineering, Indian Institute of Technology, Madras, Chennai, TN, 600036, India

    Chandrasekhar Annavarapu

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  1. Wen Jiang
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  2. Yingjie Liu
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  3. Chandrasekhar Annavarapu
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Correspondence to Chandrasekhar Annavarapu.

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Jiang, W., Liu, Y. & Annavarapu, C. A weighted Nitsche’s method for interface problems with higher-order simplex elements. Comput Mech 69, 1115–1129 (2022). https://doi.org/10.1007/s00466-021-02132-z

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