Unconditionally Monotone Schemes for Unsteady Convection-Diffusion Problems

Afanas’eva, N. M.; Churbanov, Alexander; Vabishchevich, Petr N.

doi:10.1515/cmam-2013-0002

Cited by 7 publications

(1 citation statement)

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“…[24,30] The second possibility to check the a priori estimate (14) is associated with the use of the concept of the logarithmic norm. [31,32] For the right-hand side, we have…”

Section: Time-stepping Techniquesmentioning

confidence: 99%

Computational algorithms for solving the coefficient inverse problem for parabolic equations

Vabishchevich

Васильев

2014

Inverse Problems in Science and Engineering

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Among inverse problems for partial differential equations, we distinguish coefficient inverse problems, which are associated with the identification of coefficients and/or the right-hand side of an equation using some additional information. When considering time-dependent problems, the identification of the coefficient dependences on space and on time is usually separated into individual problems. In some cases, we have linear inverse problems (e.g. identification problems for the right-hand side of an equation); this situation essentially simplify their study. This work deals with the problem of determining in a multidimensional parabolic equation the lower coefficient that depends on time only. To solve numerically a non-linear inverse problem, linearized approximations in time are constructed using standard finite difference approximations in space. The computational algorithm is based on a special decomposition, where the transition to a new time level is implemented via solving two standard elliptic problems.

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“…[24,30] The second possibility to check the a priori estimate (14) is associated with the use of the concept of the logarithmic norm. [31,32] For the right-hand side, we have…”

Section: Time-stepping Techniquesmentioning

confidence: 99%