지원사업
학술연구/단체지원/교육 등 연구자 활동을 지속하도록 DBpia가 지원하고 있어요.
커뮤니티
연구자들이 자신의 연구와 전문성을 널리 알리고, 새로운 협력의 기회를 만들 수 있는 네트워킹 공간이에요.
논문 기본 정보
- 자료유형
- 학술저널
- 저자정보
- 저널정보
- 한국산업응용수학회 JOURNAL OF THE KOREAN SOCIETY FOR INDUSTRIAL AND APPLIED MATHEMATICS Journal of the Korean Society for Industrial and Applied Mathematics Vol.23 No.2
- 발행연도
- 2019.6
- 수록면
- 65 - 92 (28page)
이용수
초록· 키워드
오류제보하기
We survey a recently developed immersed finite element method (IFEM) for the interface problems. The IFEM uses structured grids such as uniform grids, even if the interface is a smooth curve. Instead of fitting the curved interface, the bases are modified so that they satisfy the jump conditions along the interface.
The early versions of IFEM [1, 2] were suboptimal in convergence order [3]. Later, the consistency terms were added to the bilinear forms [4, 5], thus the scheme became optimal and the error estimates were proven.
For elasticity problems with interfaces, we modify the Crouzeix-Raviart based element to satisfy the traction conditions along the interface [6], but the consistency terms are not needed. To satisfy the Korn’s inequality, we add the stabilizing terms to the bilinear form. The optimal error estimate was shown for a triangular grid.
Lastly, we describe the multigrid algorithms for the discretized system arising from IFEM. The prolongation operators are designed so that the prolongated function satisfy the flux continuity condition along the interface. The W-cycle convergence was proved, and the number of V-cycle is independent of the mesh size.
The early versions of IFEM [1, 2] were suboptimal in convergence order [3]. Later, the consistency terms were added to the bilinear forms [4, 5], thus the scheme became optimal and the error estimates were proven.
For elasticity problems with interfaces, we modify the Crouzeix-Raviart based element to satisfy the traction conditions along the interface [6], but the consistency terms are not needed. To satisfy the Korn’s inequality, we add the stabilizing terms to the bilinear form. The optimal error estimate was shown for a triangular grid.
Lastly, we describe the multigrid algorithms for the discretized system arising from IFEM. The prolongation operators are designed so that the prolongated function satisfy the flux continuity condition along the interface. The W-cycle convergence was proved, and the number of V-cycle is independent of the mesh size.
목차
ABSTRACT
1. INTRODUCTION
2. SCALAR ELLIPTIC PROBLEMS
3. ELASTICITY EQUATION
4. MULTIGRID ALGORITHMS
REFERENCES
참고문헌 (48)
참고문헌 신청
Z. LI / 2003 / New cartesian grid methods for interface problems using the finite element formulation / Numerische Mathematik 96:61~98
Z. LI / 2004 / An immersed finite element space and its approximation capability / Numerical Methods for Partial Differential Equations 20:338~367
H. JI / 2014 / A symmetric and consistent immersed finite element method for interface problems / Journal of Scientific Computing 61:533~557
T. LIN / 2015 / Partially penalized immersed finite element methods for elliptic interface problems / SIAM Journal on Numerical Analysis 53:1121~1144
D. Y. KWAK / 2015 / A modified P1-immersed finite element metho / International Journal of Pure and Applied Mathematics 104:471~494
Z. LI / 2004 / An immersed finite element space and its approximation capability / Numerical Methods for Partial Differential Equations 20:338~367
H. JI / 2014 / A symmetric and consistent immersed finite element method for interface problems / Journal of Scientific Computing 61:533~557
T. LIN / 2015 / Partially penalized immersed finite element methods for elliptic interface problems / SIAM Journal on Numerical Analysis 53:1121~1144
D. Y. KWAK / 2015 / A modified P1-immersed finite element metho / International Journal of Pure and Applied Mathematics 104:471~494
함께 읽어보면 좋을 논문
논문 유사도에 따라 DBpia 가 추천하는 논문입니다. 함께 보면 좋을 연관 논문을 확인해보세요!
-
A CONSISTENT DISCONTINUOUS BUBBLE SCHEME FOR ELLIPTIC PROBLEMS WITH INTERFACE JUMPS
JOURNAL OF THE KOREAN SOCIETY FOR INDUSTRIAL AND APPLIED MATHEMATICS
2020 .06
-
Current-induced magnetization change in a ferromanget/Ge₂Sb₂Te5 interface
한국자기학회 학술연구발표회 논문개요집
2019 .05
-
Characteristics of Interface States in One-dimensional Composite Photonic Structures
Current Optics and Photonics
2022 .06
-
SPECTRAL LEGENDRE AND CHEBYSHEV APPROXIMATION FOR THE STOKES INTERFACE PROBLEMS
JOURNAL OF THE KOREAN SOCIETY FOR INDUSTRIAL AND APPLIED MATHEMATICS
2017 .09
-
Surface and interface as foundation to realizing designer materials
한국진공학회 학술발표회초록집
2016 .08
-
Study of electronic structures of ZnO thin film at the interface with 2D materials
한국진공학회 학술발표회초록집
2016 .08
-
Antimicrobial Resistance at the Humans, Animals, and Environment Interface
한국미생물학회 학술대회논문집
2018 .04
-
Iron at the Interface of Infection and Immunity
한국미생물학회 학술대회논문집
2017 .04
-
Tunable magnetic properties via interface engineering
한국자기학회 학술연구발표회 논문개요집
2019 .11
-
Engineering quantum phenomena and electronic structures on oxide interfaces
한국자기학회 학술연구발표회 논문개요집
2024 .11
-
Development of new interfacing compounds for ultra-stable biosensors
한국진공학회 학술발표회초록집
2020 .08
-
Computational studies on geometric and electronic structures at organic-metal interfaces
한국진공학회 학술발표회초록집
2016 .08
-
A study on interface layer using carbons-metal composite of ionic polymer metal composite
한국진공학회 학술발표회초록집
2020 .02
-
ROBUST A POSTERIORI ERROR ESTIMATOR FOR LOWEST-ORDER FINITE ELEMENT METHODS OF INTERFACE PROBLEMS
JOURNAL OF THE KOREAN SOCIETY FOR INDUSTRIAL AND APPLIED MATHEMATICS
2016 .06
-
Enhanced Superconductivity of Sr₂RuO₄ and La2-xSrxCuO₄ Thin Films by Atomic-Scale Interface Engineering
한국자기학회 학술연구발표회 논문개요집
2021 .11
-
Interface & additive engineering for high-performance perovskite solar cells
한국진공학회 학술발표회초록집
2020 .02
-
Coupled spin-charge transport in oxide interface
한국자기학회 학술연구발표회 논문개요집
2020 .07
-
Coupled spin-charge transport in oxide interface
한국자기학회 학술연구발표회 논문개요집
2019 .11
-
Liquid interface investigation with energetic ion beams
한국진공학회 학술발표회초록집
2016 .08
-
Spin and Charge conversion study at functional low dimensional oxide interface
한국자기학회 학술연구발표회 논문개요집
2024 .05
이 논문의 저자 정보
최근 본 자료
댓글(0)
0
UCI(KEPA) : I410-ECN-0101-2019-410-000881519