1 |
K. GARRETT AND H. ROSENBERG, The thermal conductivity of epoxy-resin/powder composite materials, Journal of Physics D: Applied Physics, 7 (1974), p. 1247.
DOI
|
2 |
T. BELYTSCHKO, N. MOES, S. USUI, AND C. PARIMI, Arbitrary discontinuities in finite elements, International Journal for Numerical Methods in Engineering, 50 (2001), pp. 993-1013.
DOI
|
3 |
Z. HASHIN, Thin interphase/imperfect interface in elasticity with application to coated fiber composites, Journal of the Mechanics and Physics of Solids, 50 (2002), pp. 2509-2537.
DOI
|
4 |
A. BUFFA, Remarks on the discretization of some noncoercive operator with applications to heterogeneous maxwell equations, SIAM Journal on Numerical Analysis, 43 (2005), pp. 1-18.
DOI
|
5 |
Z. CHEN, Reservoir simulation: mathematical techniques in oil recovery, SIAM, 2007.
|
6 |
H. DUAN AND B. L. KARIHALOO, Effective thermal conductivities of heterogeneous media containing multiple imperfectly bonded inclusions, Physical Review B, 75 (2007), p. 064206.
DOI
|
7 |
F. PAVANELLO, F. MANCA, P. LUCA PALLA, AND S. GIORDANO, Generalized interface models for transport phenomena: Unusual scale effects in composite nanomaterials, Journal of Applied Physics, 112 (2012), p. 084306.
DOI
|
8 |
R. PLONSEY, Bioelectric sources arising in excitable fibers (Alza lecture), Annals of biomedical engineering, 16 (1988), pp. 519-546.
DOI
|
9 |
M. R. HOSSAN, R. DILLON, AND P. DUTTA, Hybrid immersed interface-immersed boundary methods for ac dielectrophoresis, Journal of Computational Physics, 270 (2014), pp. 640-659.
DOI
|
10 |
G. CHAVENT AND J. JAFFRE, Mathematical models and finite elements for reservoir simulation: single phase, multiphase and multicomponent flows through porous media, Elsevier, 1986.
|
11 |
C. VAN DUIJN, J. MOLENAAR, AND M. DE NEEF, The effect of capillary forces on immiscible two-phase flow in heterogeneous porous media, Transport in Porous Media, 21 (1995), pp. 71-93.
DOI
|
12 |
M. F. WHEELER, An elliptic collocation-finite element method with interior penalties, SIAM Journal on Numerical Analysis, 15 (1978), pp. 152-161.
DOI
|
13 |
B. COCKBURN, G. E. KARNIADAKIS, AND C.-W. SHU, The development of discontinuous Galerkin methods, in Discontinuous Galerkin Methods, Springer, 2000, pp. 3-50.
|
14 |
D. N. ARNOLD, F. BREZZI, B. COCKBURN, AND L. D. MARINI, Unified analysis of discontinuous Galerkin methods for elliptic problems, SIAM journal on numerical analysis, 39 (2002), pp. 1749-1779.
DOI
|
15 |
P. KRYSL AND T. BELYTSCHKO, An efficient linear-precision partition of unity basis for unstructured meshless methods, Communications in Numerical Methods in Engineering, 16 (2000), pp. 239-255.
DOI
|
16 |
A. ERN, I. MOZOLEVSKI, AND L. SCHUH, Discontinuous Galerkin approximation of two-phase flows in heterogeneous porous media with discontinuous capillary pressures, Computer methods in applied mechanics and engineering, 199 (2010), pp. 1491-1501.
DOI
|
17 |
N. MOE S, J. DOLBOW, AND T. BELYTSCHKO, A finite element method for crack growth without remeshing, International journal for numerical methods in engineering, 46 (1999), pp. 131-150.
DOI
|
18 |
T. BELYTSCHKO AND T. BLACK, Elastic crack growth in finite elements with minimal remeshing, International journal for numerical methods in engineering, 45 (1999), pp. 601-620.
DOI
|
19 |
T. BELYTSCHKO, C. PARIMI, N. MOES, N. SUKUMAR, AND S. USUI, Structured extended finite element methods for solids defined by implicit surfaces, International journal for numerical methods in engineering, 56 (2003), pp. 609-635.
DOI
|
20 |
G. LEGRAIN, N. MOES, AND E. VERRON, Stress analysis around crack tips in finite strain problems using the extended finite element method, International Journal for Numerical Methods in Engineering, 63 (2005), pp. 290-314.
DOI
|
21 |
Z. LI, T. LIN, AND X. WU, New cartesian grid methods for interface problems using the finite element formulation, Numerische Mathematik, 96 (2003), pp. 61-98.
DOI
|
22 |
Z. LI, T. LIN, Y. LIN, AND R. C. ROGERS, An immersed finite element space and its approximation capability, Numerical Methods for Partial Differential Equations, 20 (2004), pp. 338-367.
DOI
|
23 |
S. H. CHOU, D. Y. KWAK, AND K. T. WEE, Optimal convergence analysis of an immersed interface finite element method, Advances in Computational Mathematics, 33 (2010), pp. 149-168.
DOI
|
24 |
D. Y. KWAK, K. T. WEE, AND K. S. CHANG, An analysis of a broken -nonconforming finite element method for interface problems, SIAM Journal on Numerical Analysis, 48 (2010), pp. 2117-2134.
DOI
|
25 |
D. Y. KWAK AND J. LEE, A modified -immersed finite element method, International Journal of Pure and Applied Mathematics, 104 (2015), pp. 471-494.
|
26 |
D. Y. KWAK, S. JIN, AND D. KYEONG, A stabilized -nonconforming immersed finite element method for the interface elasticity problems, ESAIM: Mathematical Modelling and Numerical Analysis, 51 (2017), pp. 187-207.
DOI
|
27 |
D. KYEONG AND D. Y. KWAK, An immersed finite element method for the elasticity problems with displacement jump, Advances in Applied Mathematics and Mechanics, 9 (2017), pp. 407-428.
DOI
|
28 |
S. JIN, D. Y. KWAK, AND D. KYEONG, A consistent immersed finite element method for the interface elasticity problems, Advances in Mathematical Physics, 2016 (2016).
|
29 |
G. JO AND D. Y. KWAK, An IMPES scheme for a two-phase flow in heterogeneous porous media using a structured grid, Computer Methods in Applied Mechanics and Engineering, (2017).
|
30 |
D. Y. KWAK, S. LEE, AND H. YUNKYONG, A new finite element for interface problems having robin type jump, Inernational Journal of Numerical Analysis and Modeling, 14 (2017), pp. 532-549.
|
31 |
J. A. ROITBERG ET AL., A theorem on homeomorphisms for elliptic systems and its applications, Mathematics of the USSR-Sbornik, 7 (1969), p. 439.
DOI
|
32 |
M. CROUZEIX AND P. A. RAVIART, Conforming and nonconforming finite element methods for solving the stationary Stokes equations I, Revue francaise d'automatique, informatique, recherche operationnelle. Mathematique, 7 (1973), pp. 33-75.
|
33 |
S. H. CHOU, D. Y. KWAK, AND K. Y. KIM, Mixed finite volume methods on nonstaggered quadrilateral grids for elliptic problems, Mathematics of computation, 72 (2003), pp. 525-539.
DOI
|
34 |
K. S. CHANG AND D. Y. KWAK, Discontinuous bubble scheme for elliptic problems with jumps in the solution, Computer Methods in Applied Mechanics and Engineering, 200 (2011), pp. 494-508.
DOI
|
35 |
T. LIN, Q. YANG, AND X. ZHANG, A priori error estimates for some discontinuous Galerkin immersed finite element methods, Journal of Scientific Computing, 65 (2015), pp. 875-894.
DOI
|
36 |
T. LIN, Y. LIN, AND X. ZHANG, Partially penalized immersed finite element methods for elliptic interface problems, SIAM Journal on Numerical Analysis, 53 (2015), pp. 1121-1144.
DOI
|
37 |
J. H. BRAMBLE AND J. T. KING, A finite element method for interface problems in domains with smooth boundaries and interfaces, Advances in Computational Mathematics, 6 (1996), pp. 109-138.
DOI
|