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 multiscale and multiphysics problems
List of Publications

S.Y. Yi, S. Lee, and L. Zikatanov, Lockingfree enriched Galerkin method for linear elasticity, SIAM Journal on Numerical Analysis accepted, 2021

S.Y. Yi, X. Hu, S. Lee, J.H. Adler, and L. Zikatanov, an enriched Galerkin method for the Stokes equations, submitted, 2021

S.Y. Yi and K. Lee, Numerical study for European option pricing equations with nonLevy jumps, Applicable Analysis, vol. 100, no. 7, pp. 14541470, 2021

Y. Jeon and S.Y. Yi, The immersed interface hybridized difference method for parabolic interface problems, in review, 2020

M.L. Bean and S.Y. Yi, A Monolithic Mixed Finite Element Method for a FluidStructure Interaction Problem, Applied Mathematics and Computation, vol. 363, 2019

S.Y. Yi, A lowestorder weak Galerkin method for linear elasticity, Journal of Compuational and Applied Mathematics, vol. 350, pp. 286298, 2019

S.Y. Yi, A study of two modes of locking in poroelasticity, SIAM Journal on Numerical Analysis, vol. 55, no. 4, pp. 19151936, 2017

M. L. Bean, K. Lipnikov, S.Y. Yi, A blockdiagonal preconditioner for a fourfield mixed fintie element method for Biot's equations, Applied Numerical Mathematics, vol. 122, pp. 113, 2017

S.Y. Yi and M. L. Bean, Iteratively coupled solution strategies for a fourfield mixed finite method for poroelasticity, International Journal for Numerial and Analytical Methods in Geomechanics, vol. 41, issue 2, pp. 159179, 2017

A. Cesmelioglu, H. Lee, A. Quaini, K. Wang, and S.Y. Yi, Optimizationbased decoupling algorithms for fluidporoelastic 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. 137176, 2016

M. Peszynska, R. E. Showalter, and S.Y. Yi, Flow and transport when scales are not separated: Numerical analysis and simulations of micro and macromodels, International Journal of Numerical Analysis and Modeling, vol. 12, no. 3, pp. 476515, 2015.

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. 8196, 2014

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 11891210, 2014

S.Y. Yi and S. Lee, An operatorsplitting method for the forced Kortewegde Vries equation, Applied Mathematics and Computation, vol. 230, pp. 276289, 2014

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. 17491777, 2013

S.Y. Yi and J. Douglas, Jr., An experimental study of several multidimensional, locally conservative, EulerianLagrangian finite element methods for a semilinear parabolic equation, International Journal of Numerical Analysis and Modeling Series B, vol. 4, no. 3, pp. 29314, 2013.

S.Y. Yi, M. Peszynska, and R. E. Showalter, Numerical upscaled model of transport with nonseparated scaes, XVIII International Conference on Water Resources, CMWR 2010, J. Carreta (Ed), Barcelona, 2010

J. Douglas, Jr., A. M. Spagnuolo, and S.Y. Yi, The Convergence of a multidimensional, locally conservative, EulerianLagrangian finite element method for a semilinear parabolic equation, Math. Models Methods Appl. Sci., 20(2), pp. 315348, 2010

M. Peszynska, R. E. Showalter, and S.Y. Yi, Homogenization of pseudoparabolic systems, Applicable Analysis, 88(9), pp. 12651282, 2009

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.126149, 2008

S.Y. Yi, A new nonconforming mixed finite element method for linear elasticity, Math. Models Methods Appl. Sci., 16(7), pp. 979999, 2006

S.Y. Yi, mixed finite element methods for llinear elasticity using rectangular elements in two and three dimensions, Calcolo, 42(2), pp. 115133, 2005
Research in Progress

(With S. Lee and L. Zikatanov) Locally conservative and lockingfree enriched Galerkin method for poroelasticity, in progress, 2021

(With C. Xiao, Y. Wang, and A. Duval) Geometric Modeling of Girus Trisymmetron, in progress, 2021,