An ADMM-Newton-CNN numerical approach to a TV model for identifying discontinuous diffusion coefﬁcients in elliptic equations: Convex case with gradient observations

A numerical approach for the segregation of atomic oxygen at Ag/MgO interfaces is presented. A general segregation kinetics is considered and the coupled system of differ- ential equations is solved due to a one-dimensional finite difference scheme which accounts for concentration-dependent diffusion coefficients. Based on a model oxide distribution, the influence of the concentration-dependency is numerically investigated and compared with the solution for constant coefficients. In addition, the numerical approach allows for the consider- ation of general boundary conditions, specimen sizes and time-dependent material and process parameters.

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Identification of Source Terms in a Coupled Age-structured Population Model with Discontinuous Diffusion Coefficients

AIMS Mathematics ◽

10.3934/math.2017.1.81 ◽

2017 ◽

Vol 2 (1) ◽

pp. 81-95

Author(s):

Varadharaj Dinakar ◽

◽

Natesan Barani Balan ◽

Krishnan Balachandran

Keyword(s):

Diffusion Coefficients ◽

Population Model ◽

Source Terms ◽

Structured Population Model ◽

Structured Population ◽

Age Structured ◽

Discontinuous Diffusion ◽

Age Structured Population

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A posteriori error estimates for mixed finite volume solution of elliptic boundary value problems

Moroccan Journal of Pure and Applied Analysis ◽

10.1515/mjpaa-2017-0016 ◽

2017 ◽

Vol 3 (2) ◽

pp. 199-217

Author(s):

Fayssal Benkhaldoun ◽

Mohammed Seaid ◽

Amadou Mahamane

Keyword(s):

Error Estimates ◽

Finite Volume ◽

Diffusion Coefficients ◽

Elliptic Equations ◽

A Posteriori Error Estimates ◽

Posteriori Error ◽

Second Order ◽

A Posteriori ◽

A Posteriori Error ◽

Second Order Elliptic Equations

AbstractThe major emphasis of this work is the derivation of a posteriori error estimates for the mixed finite volume discretization of second-order elliptic equations. The estimates are established for meshes consisting of simplices on unstructured grids. We consider diffusion problems with nonhomogeneous diffusion coefficients. The error estimates are of residual types and are formulated in the energy semi-norm for a locally postprocessed approximate solutions. The estimates are fully computable and locally efficient that they can serve as indicators for adaptive refinement and for the actual control of the error. Numerical results are shown for two test examples in two space dimensions. It is found that the proposed adaptive mixed finite volume method offers a robust and accurate approach for solving second-order elliptic equations, even when highly nonhomogeneous diffusion coefficients are used in the simulations.

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