(A) discontinuous galerkin method for elliptic interface problems = 타원형 경계문제의 불연속 galerkin 방법에 관한 연구

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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.
Advisors
Lee, Chang-Ockresearcher이창옥researcher
Description
한국과학기술원 : 응용수학전공,
Publisher
한국과학기술원
Issue Date
2004
Identifier
240349/325007  / 020024025
Language
eng
Description

학위논문(석사) - 한국과학기술원 : 응용수학전공, 2004.8, [ vi, 49 p. ]

Keywords

DISCONTINUOUS GALERKINNS; ELLIPTIC INTERFACE PROBLEM; BLENDING; 불연속 GALERKIN; 타원형 경계문제; WARPING SYMMETRY

URI
http://hdl.handle.net/10203/42109
Link
http://library.kaist.ac.kr/search/detail/view.do?bibCtrlNo=240349&flag=dissertation
Appears in Collection
MA-Theses_Master(석사논문)
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