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Your search keyword '"Li-Yeng Sung"' showing total 165 results
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165 results on '"Li-Yeng Sung"'

1. Multigrid methods for an elliptic optimal control problem with pointwise state constraints

Author

Susanne C. Brenner, Sijing Liu, and Li-yeng Sung

Subjects
Elliptic distributed optimal control problems, Pointwise state constraints, Multigrid methods, P1 finite element method, Primal–dual active set algorithm, Mathematics, QA1-939
Abstract

We design multigrid methods for an elliptic distributed optimal control problem with pointwise state constraints. They are based on the P1 finite element method from Brenner et al. (2021), where the optimal control problem was reformulated as a variational inequality for the state variable. The performance of the multigrid methods is illustrated by numerical experiments.

Published
2023
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2. A cubic C0 interior penalty method for elliptic distributed optimal control problems with pointwise state and control constraints

Author

Susanne C. Brenner, Li-yeng Sung, and Zhiyu Tan

Subjects
Elliptic distributed optimal control problems, Pointwise state and control constraints, C0interior penalty methods, Cubic Hermite finite element, Mathematics, QA1-939
Abstract

We design and analyze a cubic C0interior penalty method for linear–quadratic elliptic distributed optimal control problems with pointwise state and control constraints. Numerical results that corroborate the theoretical error estimates are also presented.

Published
2020
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31. A C1 virtual element method for an elliptic distributed optimal control problem with pointwise state constraints

Author

Susanne C. Brenner, Zhiyu Tan, and Li-Yeng Sung

Subjects
Pointwise, Computer science, Applied Mathematics, Modeling and Simulation, Applied mathematics, State (functional analysis), Element (category theory), Optimal control
Abstract

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.

Published
2021

38. A convexity enforcing $${C}^{{0}}$$ interior penalty method for the Monge–Ampère equation on convex polygonal domains

Author

Zhiyu Tan, Li-Yeng Sung, Hongchao Zhang, and Susanne C. Brenner

Subjects
Computational Mathematics, Applied Mathematics, Numerical analysis, Regular polygon, Applied mathematics, A priori and a posteriori, Monge–Ampère equation, Penalty method, Boundary value problem, Convexity, Finite element method, Mathematics
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.

Published
2021

39. A 𝑃1 Finite Element Method for a Distributed Elliptic Optimal Control Problem with a General State Equation and Pointwise State Constraints

Author

Susanne C. Brenner, Li-Yeng Sung, and Sijing Liu

Subjects
Pointwise, General state, Computational Mathematics, Numerical Analysis, Applied Mathematics, Applied mathematics, State (functional analysis), Optimal control, Finite element method, 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.

Published
2021

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