The immersed interface method for two-dimensional heat-diffusion equations with singular own sources

Kandilarov, Juri D.; Vulkov, Lubin G.

doi:10.1016/j.apnum.2006.07.002

Cited by 25 publications

(23 citation statements)

References 16 publications

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“…It has been successfully implemented for 1D and 2D linear and nonlinear elliptic and parabolic equations. Some 2D problems with jump conditions, that depend on the solution on the interface are considered by Kandilarov and Vulkov [7,9,10,15]. In [1] the IIM for parabolic-elliptic problem was studied.…”

Section: U(x Y T) = U B (X Y T) (X Y T) In ∂ω ×mentioning

confidence: 99%

A Coupling Interface Method for a Nonlinear Parabolic-Elliptic Problem

Kandilarov

2009

Lecture Notes in Computer Science

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Abstract.A coupling interface method (CIM) on uniform cartesian grid for solving parabolic-elliptic problems is proposed. The domain Ω is divided in two subregions Ω − and Ω + . On Ω − we consider an elliptic equation with nonlinear term and on Ω + -a linear parabolic equation. On the interface Γ the standard transmission conditions are stated: the jumps of the solution and the flux are zero. A method of upper and lower solutions is used to deal with the nonlinearity. Numerical experiments are discussed.

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Section: U(x Y T) = U B (X Y T) (X Y T) In ∂ω ×mentioning

confidence: 99%

A Coupling Interface Method for a Nonlinear Parabolic-Elliptic Problem

Kandilarov

2009

Lecture Notes in Computer Science

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“…The problem (1)- (6) arises, when we study the production of eddy currents in a metallic cylinder due to particular type of external electromagnetic field as a special case, see [1]. Existence and uniqueness of the solution has been studied by MacCamy and Suri [11] and Al-Droubi [2].…”

Section: X(s) Y(s) T) − U − (X(s) Y(s) T) = ϕ(X(s) Y(s) T)mentioning

confidence: 99%

Immersed Interface Difference Schemes for a Parabolic-Elliptic Interface Problem

Brayanov

Kandilarov

Koleva

2008

Large-Scale Scientific Computing

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Abstract. Second order immersed interface difference schemes for a parabolic-elliptic interface problem arising in electromagnetism is presented. The numerical method uses uniform Cartesian meshes. The standard schemes are modified near the interface curve taking into account the specific jump conditions for the solution and the flux. Convergence of the method is discussed and numerical experiments, confirming second order of accuracy are shown.

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“…The error at the mesh points satisfies 12) where the constant C is independent of h, h = max{h 1 , h 2 }.…”

Section: Discrete Mp and Convergencementioning

confidence: 99%

“…The interface problems are objects of intensive investigations and numerical methods construction during the past years, see [1,2,3,4,5,9,10,11,12,13,14,18] and references given there. In [1], the solution of a general interface problem is reduced to the solution of simpler interface problems of type (PC), (OCS).…”

Section: Introduction and Problem Formulationmentioning

confidence: 99%

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Finite Element Solution of Boundary Value Problems With Nonlocal Jump Conditions

Koleva¹

2008

Mathematical Modelling and Analysis

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Abstract. We consider stationary linear problems on non-connected layers with distinct material properties. Well posedness and the maximum principle (MP) for the differential problems are proved. A version of the finite element method (FEM) is used for discretization of the continuous problems. Also, the MP and convergence for the discrete solutions are established. An efficient algorithm for solution of the FEM algebraic equations is proposed. Numerical experiments for linear and nonlinear problems are discussed.

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The immersed interface method for two-dimensional heat-diffusion equations with singular own sources

Cited by 25 publications

References 16 publications

A Coupling Interface Method for a Nonlinear Parabolic-Elliptic Problem

A Coupling Interface Method for a Nonlinear Parabolic-Elliptic Problem

Immersed Interface Difference Schemes for a Parabolic-Elliptic Interface Problem

Finite Element Solution of Boundary Value Problems With Nonlocal Jump Conditions

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