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Creators/Authors contains: "Lee, Jeonghun J."

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  1. ; ; ; (, Computers mathematics with applications)
    We introduce and analyze a coupled hybridizable discontinuous Galerkin/discontinuous Galerkin (HDG/DG) method for porous media in which we allow fully and partly immersed faults, and faults that separate the domain into two disjoint subdomains. We prove well-posedness and present an a priori error analysis of the discretization. Numerical examples verify our analysis. 
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    Free, publicly-accessible full text available December 15, 2026
  2. (, Computers and mathematics with applications)
    In this work we develop an a posteriori error estimator for mixed finite element methods of Darcy flow problems with Robin-type jump interface conditions. We construct an energy-norm type a posteriori error estimator using the Stenberg post-processing. The reliability of the estimator is proved using an interface-adapted Helmholtz-type decomposition and an interface-adapted Scott-Zhang type interpolation operator. A local efficiency and the reliability of post-processed pressure are also proved. Numerical results illustrating adaptivity algorithms using our estimator are included. 
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    Free, publicly-accessible full text available November 15, 2025
  3. ; ; (, ESAIM: Mathematical Modelling and Numerical Analysis)
    In this paper we present a hybridizable discontinuous Galerkin method for the time-dependent Navier–Stokes equations coupled to the quasi-static poroelasticity equationsviainterface conditions. We determine a bound on the data that guarantees stability and well-posedness of the fully discrete problem and provea priorierror estimates. A numerical example confirms our analysis. 
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  4. ; (, Journal of Computational and Applied Mathematics)
    We develop mixed finite element methods for nonlinear reaction–diffusion equations with interfaces which have Robin-type interface conditions. We introduce the velocity of chemicals as new variables and reformulate the governing equations. The stability of semidiscrete solutions, existence and the a priori error estimates of fully discrete solutions are proved by fixed point theorem and continuous/discrete Gronwall inequalities. Numerical results illustrating our theoretical analysis are included. 
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  5. ; ; ; (, Computers & Mathematics with Applications)
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  6. ; ; (, ESAIM: Mathematical Modelling and Numerical Analysis)
    We present a strongly conservative and pressure-robust hybridizable discontinuous Galerkin method for the coupled time-dependent Navier–Stokes and Darcy problem. We show existence and uniqueness of a solution and present an optimala priorierror analysis for the fully discrete problem when using Backward Euler time stepping. The theoretical results are verified by numerical examples. 
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  7. ; (, Computers & Mathematics with Applications)
    In this paper we propose a variant of enriched Galerkin methods for second order elliptic equations with over-penalization of interior jump terms. The bilinear form with interior over-penalization gives a non-standard norm which is different from the discrete energy norm in the classical discontinuous Galerkin methods. Nonetheless we prove that optimal a priori error estimates with the standard discrete energy norm can be obtained by combining a priori and a posteriori error analysis techniques. We also show that the interior over-penalization is advantageous for constructing preconditioners robust to mesh refinement by analyzing spectral equivalence of bilinear forms. Numerical results are included to illustrate the convergence and preconditioning results. 
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  8. ; ; (, Journal of Scientific Computing)
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  9. ; ; (, Computers & Mathematics with Applications)
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  10. ; ; ; (, Computers & Mathematics with Applications)
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