54 citations · 150 across the 13 of their papers we have counts for
15 papers
--Nonconforming Quadrilateral Finite Element Space with Periodic Boundary Conditions: Part II. Application to the Nonconforming Heterogeneous Multiscale Method
Jaeryun Yim, Dongwoo Sheen, Imbo Sim
A homogenization approach is one of effective strategies to solve multiscale elliptic problems approximately. The finite element heterogeneous multiscale method (FEHMM) which is ba…
--Nonconforming Quadrilateral Finite Element Space with Periodic Boundary Conditions: Part I. Fundamental results on dimensions, bases, solvers, and error analysis
Jaeryun Yim, Dongwoo Sheen
The --nonconforming quadrilateral finite element space with periodic boundary condition is investigated. The dimension and basis for the space are characterized with the conce…
Simple quadrature rules for a nonparametric nonconforming quadrilateral element
Kanghun Cho, Dongwoo Sheen
We introduce simple quadrature rules for the family of nonparametric nonconforming quadrilateral element with four degrees of freedom. Our quadrature rules are motivated by the wor…
Algebraic Multiscale Method for one--dimensional elliptic problems
Kanghun Cho, Roktaek Lim, Dongwoo Sheen
In this paper we propose an idea of constructing a macro--scale matrix system given a micro--scale matrix linear system. Then the macro--scale system is solved at cheaper computing…
A computational macroscale model for the time fractional poroelasticity problem in fractured and heterogeneous media
Aleksei Tyrylgin, Maria Vasilyeva, Anatoly Alikhanov +1
In this work, we introduce a time memory formalism in poroelasticity model that couples the pressure and displacement. We assume this multiphysics process occurs in multicontinuum…
A nonconforming immersed finite element method for elliptic interface problems
Tao Lin, Dongwoo Sheen, Xu Zhang
A new immersed finite element (IFE) method is developed for second-order elliptic problems with discontinuous diffusion coefficient. The IFE space is constructed based on the rotat…
Error Estimates for Approximations of Distributed Order Time Fractional Diffusion with Nonsmooth Data
Bangti Jin, Raytcho Lazarov, Dongwoo Sheen +1
In this work, we consider the numerical solution of an initial boundary value problem for the distributed order time fractional diffusion equation. The model arises in the mathemat…
Stable cheapest nonconforming finite elements for the Stokes equations
Sihwan Kim, Jaeryun Yim, Dongwoo Sheen
We introduce two pairs of stable cheapest nonconforming finite element space pairs to approximate the Stokes equations. One pair has each component of its velocity field to be appr…
Nonconforming finite element method applied to the driven cavity problem
Roktaek Lim, Dongwoo Sheen
A cheapest stable nonconforming finite element method is presented for solving the incompressible flow in a square cavity without smoothing the corner singularities. The stable che…
A new cubic nonconforming finite element on rectangles
Zhaoliang Meng, Zhongxuan Luo, Dongwoo Sheen
A new nonconforming rectangle element with cubic convergence for the energy norm is introduced. The degrees of freedom (DOFs) are defined by the twelve values at the three Gauss po…
Convergence analysis of a family of 14-node brick elements
Zhaoliang Meng, Zhongxuan Luo, Dongwoo Sheen +1
In this paper, we will give convergence analysis for a family of 14-node elements which was proposed by I. M. Smith and D. J. Kidger in 1992. The 14 DOFs are taken as the value at…
A class of nonparametric DSSY nonconforming quadrilateral elements
Youngmok Jeon, Hyun Nam, Dongwoo Sheen +1
A new class of nonparametric nonconforming quadrilateral finite elements is introduced which has the midpoint continuity and the mean value continuity at the interfaces of elements…
Turing Instability for a Ratio-Dependent Predator-Prey Model with Diffusion
Shaban Aly, Imbunm Kim, Dongwoo Sheen
Ratio-dependent predator-prey models have been increasingly favored by field ecologists where predator-prey interactions have to be taken into account the process of predation sear…
F. John's stability conditions vs. A. Carasso's SECB constraint for backward parabolic problems
Jinwoo Lee, Dongwoo Sheen
In order to solve backward parabolic problems F. John [{\it Comm. Pure. Appl. Math.} (1960)] introduced the two constraints "" and where …
Laplace transformation method for the Black-Scholes equation
Hyoseop Lee, Dongwoo Sheen
In this paper we apply the innovative Laplace transformation method introduced by Sheen, Sloan, and Thomée (IMA J. Numer. Anal., 2003) to solve the Black-Scholes equation. The algo…