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.)

1. Hyeokjoo Park, Woonsang Choi, Young-Ju Lee and Gwanghyun Jo*, Enriched Galerkin method for the heat transfer on domain with imperfect contact, accepted.

2. Gwanghyun Jo, Hyeokjoo Park and Deok-Kyu Jang*, A localized basis structure in physics-informed neural network for solving elliptic problems, accepted.

3. Hyeokjoo Park, On the approximation capability of shallow and deep neural networks having smooth activations with respect to the Sobolev norm, Neural Netw., 201 (2026), Paper No. 108935, 7 pp.

4. 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.

5. 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.

6. 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.

7. 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.

8. 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.

9. 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.

10. 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.

11. 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. 

12. 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.

13. 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.

1. Hyeokjoo Park and Gwanghyun Jo*, Locally conservative discontinous bubble scheme for multiphase flows with discontinuous capillary pressures, submitted.

2. Eun-Jae Park and Hyeokjoo Park*, Broken virtual element methods for the elliptic interface problem on unfitted polygonal meshes, submitted.

3. David Mora, Eun-Jae Park*, Hyeokjoo Park, and Alberth Silgado, C1-conforming virtual element methods for the stationary two-layer quasi-geostrophic equations of the ocean, submitted. (preprint)

4. Shuxuan Liang, Hyeokjoo Park, and Gwanghyun Jo, A deep Nitsche method for the elliptic interface problem with implicit jump conditions, submitted.

5. Hyeokjoo Park and Eun-Jae Park, Raviart–Thomas Staggered DG methods for the second-order elliptic eigenvalue problem, submitted.

6. Hyeokjoo Park and Do Y. Kwak, A mixed finite volume method for the elasticity: weak stress symmetry without multipliers, submitted.