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Creators/Authors contains: "Zhong, Liuqiang"

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  1. ; ; ; ; (, Journal of Computational and Applied Mathematics)
    Free, publicly-accessible full text available December 1, 2025
  2. ; ; ; ; (, Journal of Computational and Applied Mathematics)
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  3. ; ; ; ; (, Journal of Scientific Computing)
    In this paper, we design and analyze the conforming and nonconforming virtual element methods for the Signorini problem. Under some regularity assumptions, we prove optimal order a priori error estimates in the energy norm for both two numerical schemes. Extensive numerical tests are presented, verifying the theory and exploring unknown features. 
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  4. ; ; (, Journal of Computational Mathematics)
    A mixed finite element method is presented for the Biot consolidation problem in poroelasticity. More precisely, the displacement is approximated by using the Crouzeix-Raviart nonconforming finite elements, while the fluid pressure is approximated by using the node conforming finite elements. The well-posedness of the fully discrete scheme is established, and a corresponding priori error estimate with optimal order in the energy norm is also derived. Numerical experiments are provided to validate the theoretical results. 
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  5. ; ; ; ; (, Advances in Computational Mathematics)
    null (Ed.)
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  6. ; ; ; (, Numerical Methods for Partial Differential Equations)
    Abstract An adaptive modified weak Galerkin method (AmWG) for an elliptic problem is studied in this article, in addition to its convergence and optimality. The modified weak Galerkin bilinear form is simplified without the need of the skeletal variable, and the approximation space is chosen as the discontinuous polynomial space as in the discontinuous Galerkin method. Upon a reliable residual‐baseda posteriorierror estimator, an adaptive algorithm is proposed together with its convergence and quasi‐optimality proved for the lowest order case. The primary tool is to bridge the connection between the modified weak Galerkin method and the Crouzeix–Raviart nonconforming finite element. Unlike the traditional convergence analysis for methods with a discontinuous polynomial approximation space, the convergence of AmWG is penalty parameter free. Numerical results are presented to support the theoretical results. 
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