서지주요정보
(A) discontinuous galerkin method for elliptic interface problems = 타원형 경계문제의 불연속 galerkin 방법에 관한 연구
서명 / 저자 (A) discontinuous galerkin method for elliptic interface problems = 타원형 경계문제의 불연속 galerkin 방법에 관한 연구 / Guyomarc'h Gregory.
저자명 Gregory, Guyomarc'h
발행사항 [대전 : 한국과학기술원, 2004].
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소장정보

등록번호

8015625

소장위치/청구기호

학술문화관(문화관) 보존서고

MMA 04030

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초록정보

In this thesis, we study the possibility of applying discontinuous Galerkin (DG) methods to elliptic interface problems. This problem arises, for example, in two-phase flow simulations when the projection method is used to solve for the pressure. The main characteristic of interface problems is that the solutions are discontinuous and so are their derivatives. The discontinuities are in fact prescribed on an interface (a co-dimensional manifold). Here, we assume we have a triangulation of the computational domain that perfectly fits this interface. A standard way to solve this problem with finite element methods is to enforce the discontinuity of the solution in the finite element space. The method presented here differs from such methods in that all conditions (Dirichlet and jump conditions) are implemented weakly. We show that the method is optimally convergent in the $L^2$ -norm, and check this result by numerical experiments. Finally, we apply our method to a problem with dynamic boundary conditions. This problem arises as a significant part of the study of the electroporation phenomenon which has important applications to gene therapy and cancer treatment.

이 논문에서는 타원형 경계문제에 대한 불연속 Galerkin 방법(discontinuous Galerkin Method)의 적용가능성을 연구한다.

서지기타정보

서지기타정보
청구기호 {MMA 04030
형태사항 vi, 49 p. : 삽도 : 26 cm
언어 영어
일반주기 Appendix : Properties of sobolev spaces
지도교수의 영문표기 : Chang-Ock Lee
지도교수의 한글표기 : 이창옥
학위논문 학위논문(석사) - 한국과학기술원 : 응용수학전공,
서지주기 Reference : p. 46-49
주제 ELLIPTIC INTERFACE PROBLEM
DISCONTINUOUS GALERKINNS
BLENDING
WARPING SYMMETRY
타원형 경계문제
불연속 GALERKIN
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