Open AccessSimultaneously Identify the Leading Coefficient and Right-hand Side in a Parabolic Equation
Author(s) -
Ling De Su,
В. И. Васильев,
Tongsong Jiang
Publication year - 2020
Publication title -
journal of physics. conference series
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.21
H-Index - 85
eISSN - 1742-6596
pISSN - 1742-6588
DOI - 10.1088/1742-6596/1624/3/032008
Subject(s) - mathematics , inverse problem , nonlinear system , quadratic equation , finite element method , term (time) , scheme (mathematics) , parabolic partial differential equation , mathematical analysis , space (punctuation) , domain (mathematical analysis) , inverse , partial differential equation , computer science , geometry , physics , quantum mechanics , thermodynamics , operating system
In this article, we propose a new method for the numerical solution of a kind of coefficient inverse problem, in which the time dependent leading coefficient and the right hand side in a parabolic equation need to be identified simultaneously, based on additional information of the solutions at interior points in the computational domain. To solve the nonlinear problem, we use linearized second-order scheme for linearizing the quadratic nonlinear term in time and finite element approximation is used in the space. Based on a special decomposition, at new time level, the original problem is transformed into three standard elliptic problems. The results of numerical experiments are presented to confirm the capability and efficiency of the proposed computational algorithm.