Research Interests

My general research interests are in Numerical Analysis and Scientific Computing. My primary research interests include
  • Numerical methods for partial differential equations
  • Flow and transport in porous media
  • Computational solid mechanics
  • Modeling of multi-scale and multi-physics problems

List of Publications

  1. S.-Y. Yi, S. Lee, and L. Zikatanov, Locking-free enriched Galerkin method for linear elasticity, SIAM Journal on Numerical Analysis accepted, 2021
  2. S.-Y. Yi, X. Hu, S. Lee, J.H. Adler, and L. Zikatanov, an enriched Galerkin method for the Stokes equations, submitted, 2021
  3. S.-Y. Yi and K. Lee, Numerical study for European option pricing equations with non-Levy jumps, Applicable Analysis, vol. 100, no. 7, pp. 1454--1470, 2021
  4. Y. Jeon and S.-Y. Yi, The immersed interface hybridized difference method for parabolic interface problems, in review, 2020
  5. M.L. Bean and S.-Y. Yi, A Monolithic Mixed Finite Element Method for a Fluid-Structure Interaction Problem, Applied Mathematics and Computation, vol. 363, 2019
  6. S.-Y. Yi, A lowest-order weak Galerkin method for linear elasticity, Journal of Compuational and Applied Mathematics, vol. 350, pp. 286--298, 2019
  7. S.-Y. Yi, A study of two modes of locking in poroelasticity, SIAM Journal on Numerical Analysis, vol. 55, no. 4, pp. 1915--1936, 2017
  8. M. L. Bean, K. Lipnikov, S.-Y. Yi, A block-diagonal preconditioner for a four-field mixed fintie element method for Biot's equations, Applied Numerical Mathematics, vol. 122, pp. 1--13, 2017
  9. S.-Y. Yi and M. L. Bean, Iteratively coupled solution strategies for a four-field mixed finite method for poroelasticity, International Journal for Numerial and Analytical Methods in Geomechanics, vol. 41, issue 2, pp. 159--179, 2017
  10. A. Cesmelioglu, H. Lee, A. Quaini, K. Wang, and S.-Y. Yi, Optimization-based decoupling algorithms for fluid-poroelastic system, In Topics in Numerical Partial Differential Equations and Scientific Computing, The IMA Volumes in Mathematics and its Applications 160, S.C. Brenner (ed.), pp. 137-176, 2016
  11. M. Peszynska, R. E. Showalter, and S.-Y. Yi, Flow and transport when scales are not separated: Numerical analysis and simulations of micro- and macro-models, International Journal of Numerical Analysis and Modeling, vol. 12, no. 3, pp. 476--515, 2015.
  12. M. L. Bean and S.-Y. Yi, An Immersed Interface Method for a 1D Poroelasticity Problem with Discontinuous Coefficients, Journal of Computational and Applied Mathematics, vol. 272, pp. 81--96, 2014
  13. S.-Y. Yi, Convergence analysis of a new mixed finite element method for Biot's consolidation model, Numerical Methods for Partial Differential Equations, Numerical Methods for Partial Differential Equations, vol.30, no.4, pp 1189-1210, 2014
  14. S.-Y. Yi and S. Lee, An operator-splitting method for the forced Korteweg-de Vries equation, Applied Mathematics and Computation, vol. 230, pp. 276-289, 2014
  15. S.-Y. Yi, Coupling of nonconforming and mixed finite element methods for Biot's consolidation model, Numerical Methods for Partial Differential Equations, vol. 29, pp. 1749-1777, 2013
  16. S.-Y. Yi and J. Douglas, Jr., An experimental study of several multidimensional, locally conservative, Eulerian-Lagrangian finite element methods for a semilinear parabolic equation, International Journal of Numerical Analysis and Modeling Series B, vol. 4, no. 3, pp. 29-314, 2013.
  17. S.-Y. Yi, M. Peszynska, and R. E. Showalter, Numerical upscaled model of transport with non-separated scaes, XVIII International Conference on Water Resources, CMWR 2010, J. Carreta (Ed), Barcelona, 2010
  18. J. Douglas, Jr., A. M. Spagnuolo, and S.-Y. Yi, The Convergence of a multidimensional, locally conservative, Eulerian-Lagrangian finite element method for a semilinear parabolic equation, Math. Models Methods Appl. Sci., 20(2), pp. 315-348, 2010
  19. M. Peszynska, R. E. Showalter, and S.-Y. Yi, Homogenization of pseudoparabolic systems, Applicable Analysis, 88(9), pp. 1265-1282, 2009
  20. M. Peszynska and S.-Y. Yi, Numerical methods for unsaturated flow with dynamic capillary pressure in heterogeneous porous media, International Journal of Numerical Analysis and Modeling, 5, Supp., pp.126-149, 2008
  21. S.-Y. Yi, A new nonconforming mixed finite element method for linear elasticity, Math. Models Methods Appl. Sci., 16(7), pp. 979-999, 2006
  22. S.-Y. Yi, mixed finite element methods for llinear elasticity using rectangular elements in two and three dimensions, Calcolo, 42(2), pp. 115-133, 2005

Research in Progress

  1. (With S. Lee and L. Zikatanov) Locally conservative and locking-free enriched Galerkin method for poroelasticity, in progress, 2021
  2. (With C. Xiao, Y. Wang, and A. Duval) Geometric Modeling of Girus Trisymmetron, in progress, 2021,