Numerical partial differential equations
virtual element method
finite element method
finite volume method
discontinuous Galerkin method
Scientific machine learning
physics-informed neural network
deep Ritz method
approximation capabilities of neural networks
(* Corresponding author.)
Eun-Jae Park and Hyeokjoo Park*, A parameter-robust Crouzeix-Raviart finite element method for the Brinkman model, J. Sci. Comput., 105 (2025), Paper No. 96, 23 pp.
Gwanghyun Jo and Hyeokjoo Park*, A family of even-order edge-oriented nonconforming finite elements in 2D with efficient locally conservative flux reconstruction, Comput. Math. Appl., 196 (2025), pp. 127-134.
Hyeokjoo Park and Eun-Jae Park*, On the connection between the stabilization-free polygonal element and staggered discontinuous Galerkin methods, Math. Models Methods Appl. Sci., 35 (2025), pp. 2099-2128.
Hyeokjoo Park and Gwanghyun Jo*, A physics-informed neural network based method for the nonlinear Poisson-Boltzmann equation and its error analysis, J. Comput. Phys., 522 (2025), Paper No. 113579, 14 pp.
Gwanghyun Jo and Hyeokjoo Park*, Analysis of discontinuous bubble immersed finite element methods for elliptic interface problems with nonhomogeneous interface conditions, J. Sci. Comput., 101 (2024), Paper No. 75, 25 pp.
Hyeokjoo Park and Do Y. Kwak*, An analysis of nonconforming virtual element methods on polytopal meshes with small faces, Math. Models Methods Appl. Sci., 34 (2024), pp. 571-596.
Hyeokjoo Park and Do Y. Kwak*, A nonconforming immersed virtual element method for elliptic interface problems, ESAIM Math. Model. Numer. Anal., 57 (2023), pp. 3615-3636.
Hyeokjoo Park and Do Y. Kwak*, An immersed weak Galerkin method for elliptic interface problems on polygonal meshes, Comput. Math. Appl., 147 (2023), pp. 185-201.
Do Y. Kwak* and Hyeokjoo Park, A formal construction of a divergence-free basis in nonconforming virtual element methods for the Stokes problem, Numer. Algorithms, 91 (2022), pp. 449-471.
Do Y. Kwak* and Hyeokjoo Park, Lowest-order virtual element methods for linear elasticity problems, Comput. Methods Appl. Mech. Engrg., 390 (2022), Paper No. 114448, 20 pp.
Gwanghyun Jo, Hyeokjoo Park and Deok-Kyu Jang, A localized basis structure in physics-informed neural network for solving elliptic problems, submitted.
Shuxuan Liang, Hyeokjoo Park, and Gwanghyun Jo, A deep Nitsche method for the elliptic interface problem with implicit jump conditions, submitted.
Hyeokjoo Park and Eun-Jae Park, Raviart–Thomas Staggered DG methods for the second-order elliptic eigenvalue problem, submitted.
Hyeokjoo Park, On the approximation capability of shallow and deep neural networks having smooth activations with respect to the Sobolev norms, submitted.
Hyeokjoo Park and Do Y. Kwak, A family of weakly symmetric mixed finite volume methods for the elasticity problem, submitted.