Publications

  • C.B. Davis and Y. Zhang. A partition of unity method for a fourth order variational inequality of the second kind, submitted.
  • S.B. Boyana, T. Lewis, A. Rapp, and Y. Zhang. Convergence analysis of a symmetric dual-wind discontinuous Galerkin method for a parabolic inequality, submitted.
  • T. Lewis, A. Rapp, and Y. Zhang. Further investigation of the penalty parameter for dual-wiind discontinuous Galerkin methods on elliptic second order PDEs, submitted.
  • T. Lewis, Q. Morris, and Y. Zhang. Convergence and stability analysis for approximating sublinear positone boundary value problems with multiple solutions using finite difference methods. J. Comput. Appl. Math., 404:113880, 2022.
  • J.D. Hauenstein, A.C. Liddell, S. McPherson, and Y. Zhang. Numerical algebraic geometry and semidefinite programming. Results Appl. Math., 11:100166, 2021.
  • Y. Li and Y. Zhang. Analysis of adaptive two-grid finite element algorithms for linear and nonlinear problems. SIAM J. Sci. Comput., 43(2):A908–A928, 2021.
  • X. Feng, Y. Li, and Y. Zhang. Strong convergence of a fully discrete finite element method for a class of semilinear stochastic partial differential equations with multiplicative noise. J. Comput. Math., 39:591--616, 2021.
  • X. Feng, Y. Li, and Y. Zhang. A fully discrete mixed finite element method for the stochastic Cahn-Hilliard equation with gradient-type multiplicative noise. J. Sci. Comput., 83:23, 2020.
  • F. Gao, Z. Sun, C. Wang, and Y. Zhang. A quadratic C^0 interior penalty method for the quad-curl problem. Math. Model. Anal., 25(2): 208--225, 2020.
  • T. Lewis, A. Rapp, and Y. Zhang. Convergence analysis of a symmetric dual-wind discontinuous Galerkin method on the obstacle problems. J. Math. Anal. Appl., 485, 2020.
  • J. Cui and Y. Zhang. A new analysis of discontinuous Galerkin methods for a fourth order variational inequality. Comput. Methods Appl. Mech. Engrg., 351:531--547, 2019.
  • S.C. Brenner, L.-Y. Sung, and Y. Zhang. C^0 interior penalty methods for an elliptic state-constrained optimal control problem with Neumann boundary condition. J. Comput. Appl. Math., 350:212--232, 2019.
  • X. Feng, Y. Li, and Y. Zhang. Finite element methods for the stochastic Allen-Cahn equation with gradient-type multiplicative noises. SIAM J. Numer. Anal., 55:194--216, 2017.
  • S.C. Brenner, J. Gedicke, L.-Y. Sung, and Y. Zhang. An a posteriori analysis of C^0 interior penalty methods for the obstacle problem of clamped Kirchhoff plates. SIAM J. Numer. Anal., 55:87--108, 2017.
  • S.C. Brenner, L.-Y. Sung, and Y. Zhang. Post-processing procedures for an elliptic distributed optimal control problem with pointwise state constraints. Appl. Numer. Math., 95:99--117, 2015.
  • S.C. Brenner, L.-Y. Sung, and Y. Zhang. A quadratic C^0 interior penalty method for an elliptic optimal control problem with state constraints, Recent Developments in Discontinuous Galerkin Finite Element Methods for Partial Differential Equations, IMA Volumes in Mathematics and Its Applications, 157, 2012 John H Barrett Memorial Lectures, X. Feng, O. Karakashian, and Y. Xing, eds., Springer, 2014, pp. 97--132.
  • Y. Zhang. Finite element methods for fourth order variational inequalities. Ph.D. Dissertation, Louisiana State University, Baton Rouge, LA, 2013.
  • S.C. Brenner, L.-Y. Sung, H. Zhang, and Y. Zhang. A Morley finite element method for the displacement obstacle problem of clamped Kirchhoff plates. J. Comput. Appl. Math., 254:31--42, 2013.
  • S.C. Brenner, L.-Y. Sung, H. Zhang, and Y. Zhang. A quadratic C^0 interior penalty method for the displacement obstacle problem of clamped Kirchhoff plates. SIAM J. Numer. Anal., 50:3329--3350, 2012.
  • S.C. Brenner, L.-Y. Sung, and Y. Zhang. Finite element methods for the displacement obstacle problem of clamped plates. Math. Comp., 81:1247--1262, 2012.