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arXiv · 2508.09008

Optimality of adaptive $H(\operatorname{div}\operatorname{div})$ mixed finite element methods for the Kirchhoff-Love plate bending problem

Jun Hu·Rui Ma·Min Zhang
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Abstract

This paper presents a reliable and efficient residual-based a posteriori error analysis for the symmetric $H(\operatorname{div}\operatorname{div})$ mixed finite element method for the Kirchhoff-Love plate bending problem with mixed boundary conditions. The key ingredient lies in the construction of boundary-condition-preserving complexes at both continuous and discrete levels. Additionally, the discrete symmetric $H(\operatorname{div}\operatorname{div})$ space is extended to ensure nestedness, which leads to optimality for the adaptive algorithm. Numerical examples confirm the effectiveness of the a posteriori error estimator and demonstrate the optimal convergence rate under adaptive refinements.

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Jun Hu, Rui Ma, Min Zhang. 2025-08-12. Optimality of adaptive $H(\operatorname{div}\operatorname{div})$ mixed finite element methods for the Kirchhoff-Love plate bending problem. https://arxiv.org/abs/2508.09008

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