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Creators/Authors contains: "Tan, Zhiyu"

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  1. ; ; ; ( , Communications of the American Mathematical Society)

    We construct a nonlinear least-squares finite element method for computing the smooth convex solutions of the Dirichlet boundary value problem of the Monge-Ampère equation on strictly convex smooth domains inR2{\mathbb {R}}^2. It is based on an isoparametricC0C^0finite element space with exotic degrees of freedom that can enforce the convexity of the approximate solutions.A priorianda posteriorierror estimates together with corroborating numerical results are presented.

     
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  2. ; ; ( , Comptes Rendus. Mécanique)
    A nonlinear least-squares finite element method for strong solutions of the Dirichlet boundary value problem of a two-dimensional Pucci equation on convex polygonal domains is investigated in this paper. We obtain a priori and a posteriori error estimates and present corroborating numerical results, where the discrete nonsmooth and nonlinear optimization problems are solved by an active set method and an alternating direction method with multipliers. 
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    Free, publicly-accessible full text available April 26, 2025
  3. ; ; ; ( , Computers & Mathematics with Applications)
    We consider C0 interior penalty methods for a linear-quadratic elliptic distributed optimal control problem with pointwise state constraints in two spatial dimensions, where the cost function tracks the state at points, curves and regions of the domain. Error estimates and numerical results that illustrate the performance of the methods are presented. 
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    Free, publicly-accessible full text available February 1, 2025
  4. ; ; ( , East Asian Journal on Applied Mathematics)
    We present an adaptive nonlinear least-squares finite element method for a two dimensional Pucci equation. The efficiency of the method is demonstrated by a numerical experiment. 
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  5. ; ; ( , Mathematical Models and Methods in Applied Sciences)
    We design and analyze a [Formula: see text] virtual element method for an elliptic distributed optimal control problem with pointwise state constraints. Theoretical estimates and corroborating numerical results are presented. 
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  6. ; ; ; ( , Numerische Mathematik)
    null (Ed.)
    Abstract We design and analyze a $$C^0$$ C 0 interior penalty method for the approximation of classical solutions of the Dirichlet boundary value problem of the Monge–Ampère equation on convex polygonal domains. The method is based on an enhanced cubic Lagrange finite element that enables the enforcement of the convexity of the approximate solutions. Numerical results that corroborate the a priori and a posteriori error estimates are presented. It is also observed from numerical experiments that this method can capture certain weak solutions. 
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    Full Text Available 
  7. ; ; ; ( , Numerische Mathematik)
    We design and analyze a C0 interior penalty method for the approximation of classical solutions of the Dirichlet boundary value problem of the Monge–Ampère equation on convex polygonal domains. The method is based on an enhanced cubic Lagrange finite element that enables the enforcement of the convexity of the approximate solutions. Numerical results that corroborate the a priori and a posteriori error estimates are presented. It is also observed from numerical experiments that this method can capture certain weak solutions. 
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    Accepted Manuscript Full Text Available
  8. ; ; ( , Results in Applied Mathematics)
    null (Ed.)
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