Publications
Submitted:
Erik Burman, Rebecca Durst, Miguel Fernandez, Johnny Guzman and Sijing Liu*, Estimates of discrete time derivatives for the parabolic-parabolic Robin-Robin coupling method (2024).
Erik Burman, Rebecca Durst, Miguel Fernandez, Johnny Guzman and Sijing Liu*, A second-order correction method for loosely coupled discretizations applied to parabolic-parabolic interface problems (2024).
Satyajith Bommana Boyana, Thomas Lewis, Sijing Liu* and Yi Zhang, Convergence Analysis of Novel Discontinuous Galerkin Methods for a Convection Dominated Problem (2024).
Publications:
Sijing Liu*, Robust multigrid methods for discontinuous Galerkin discretizations of an elliptic optimal control problem. Computational Methods in Applied Mathematics (2024).
Sijing Liu*, Zhiyu Tan and Yi Zhang. Discontinuous Galerkin methods for an elliptic optimal control problem with a general state equation and pointwise state constraints. Journal of Computational and Applied Mathematics 437 (2024), 115494.
Susanne C. Brenner, Sijing Liu and Li-yeng Sung. Multigrid methods for an elliptic optimal control problem with pointwise state constraints. Results in Applied Mathematics (2023).
Susanne C. Brenner, Sijing Liu and Li-yeng Sung. A P1 finite element method for a distributed elliptic optimal control problem with a general state equation and pointwise state constraints. Computational Methods in Applied Mathematics (2021).
Susanne C. Brenner, Sijing Liu and Li-yeng Sung. Multigrid methods for saddle point problems: optimality systems, Journal of Computational and Applied Mathematics 372 (2020), 112733.
Samiul Haque, Laszlo P. Kindrat, Li Zhang, Vikenty Mikheev, Daewa Kim, Sijing Liu, Jooyeon Chung, Mykhailo Kuian, Jordan E. Massad, and Ralph C. Smith. Uncertainty-enabled design of electromagnetic reflectors with integrated shape control. In Behavior and Mechanics of Multifunctional Materials and Composites XII, vol. 10596, p. 105961D. International Society for Optics and Photonics, 2018.
* Corresponding Author
In preparation:
(with Zhiyu Tan and Yi Zhang) A H1 conforming virtual element method for an elliptic optimal control problem with pointwise state constratints.
(with Zhiyu Tan) Robust multigrid methods for an optimal control problem on graded meshes.
(with Valeria Simoncini) Robust multigrid preconditioners for an optimal control problem with a convection-dominated state equation.
(with Yi Zhang) DWDG methods for an optimal control problem with a convection-dominated state equation.
Discontinuous Galerkin methods for an elliptic optimal control problem with a convection-dominated state equation and pointwise state constraints.
(with Jinjin Zhang) BDDC preconditioner for HDG discretizations of an optimal control problem.
(with Dmitriy Leykekhman) Pointwise error estimates in the finite element method for a singularly perturbed parabolic equation.