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Creators/Authors contains: "Liu, Sijing"

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  1. ; (, Journal of Scientific Computing)
    Free, publicly-accessible full text available December 1, 2025
  2. ; ; ; (, Computers & Mathematics with Applications)
    Free, publicly-accessible full text available December 1, 2025
  3. ; ; ; ; (, IMA Journal of Numerical Analysis)
    Abstract We consider a parabolic–parabolic interface problem and construct a loosely coupled prediction-correction scheme based on the Robin–Robin splitting method analyzed in [J. Numer. Math., 31(1):59–77, 2023]. We show that the errors of the correction step converge at $$\mathcal O((\varDelta t)^{2})$$, under suitable convergence rate assumptions on the discrete time derivative of the prediction step, where $$\varDelta t$$ stands for the time-step length. Numerical results are shown to support our analysis and the assumptions. 
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  4. ; ; ; ; (, Numerical Algorithms)
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  5. (, Computational Methods in Applied Mathematics)
    Abstract We consider discontinuous Galerkin methods for an elliptic distributed optimal control problem, and we propose multigrid methods to solve the discretized system.We prove that the 𝑊-cycle algorithm is uniformly convergent in the energy norm and is robust with respect to a regularization parameter on convex domains.Numerical results are shown for both 𝑊-cycle and 𝑉-cycle algorithms. 
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  6. ; ; (, Results in Applied Mathematics)
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  7. ; ; (, Computational Methods in Applied Mathematics)
    Abstract We investigate a P 1 P_{1} finite element method for an elliptic distributed optimal control problem with pointwise state constraints and a state equation that includes advective/convective and reactive terms.The convergence of this method can be established for general polygonal/polyhedral domains that are not necessarily convex.The discrete problem is a strictly convex quadratic program with box constraints that can be solved efficiently by a primal-dual active set algorithm. 
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  8. ; ; (, Journal of computational and applied mathematics)
    We develop multigrid methods for an elliptic distributed optimal control problem on convex domains that are robust with respect to a regularization parameter. We prove the uniform convergence of the $$W$$-cycle algorithm and demonstrate the performance of $$V$$-cycle and $$W$$-cycle algorithms through numerical experiments. 
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