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A Robust Discrete Scheme based on Staggered Grids for Poroelastic-Elastic Coupled Problems

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Abstract

This paper aims to explore a robust and efficient discrete scheme for poroelastic-elastic coupled problems. Based on staggered grids, a discrete scheme using finite difference methods is constructed in a form similar to domain decomposition. On this basis, another discrete scheme with a uniform form over the entire domain is derived. These two discrete schemes serve different purposes and are shown to be equivalent. The stability is easily derived by establishing a discrete variational formulation. To prove the convergence, appropriate discrete interpolations are introduced. It is proved that the discrete scheme has second-order superconvergence. Then, combined with the inf-sup condition, the first-order uniform convergence is obtained. This means the discrete scheme has great potential to overcome Poisson locking and pressure oscillations. Some numerical experiments are also carried out, and the results show the robustness and efficiency of the discrete scheme.

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Funding

The work is supported by the National Natural Science Foundation of China Grant No.12131014.

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  1. School of Mathematics, Shandong University, Jinan, 250100, China

    Bohan Yang & Hongxing Rui

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  1. Bohan Yang
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  2. Hongxing Rui
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Correspondence to Hongxing Rui.

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Yang, B., Rui, H. A Robust Discrete Scheme based on Staggered Grids for Poroelastic-Elastic Coupled Problems. J Sci Comput 95, 25 (2023). https://doi.org/10.1007/s10915-023-02149-x

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