Geodesic
Global superconvergence of finite element methods for parabolic inverse problems
Applications of Mathematics, Tome 54 (2009) no. 3, pp. 285-294.

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In this article we transform a large class of parabolic inverse problems into a nonclassical parabolic equation whose coefficients consist of trace type functionals of the solution and its derivatives subject to some initial and boundary conditions. For this nonclassical problem, we study finite element methods and present an immediate analysis for global superconvergence for these problems, on basis of which we obtain a posteriori error estimators.
DOI : 10.1007/s10492-009-0018-4
Classification : 35K10, 35R30, 65M06, 65M32, 65M60, 76R50
Keywords: inverse problem; global superconvergence; finite element method 
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Azari, Hossein; Zhang, Shuhua. Global superconvergence of finite element methods for parabolic inverse problems. Applications of Mathematics, Tome 54 (2009) no. 3, pp. 285-294. doi : 10.1007/s10492-009-0018-4. http://geodesic.mathdoc.fr/articles/10.1007/s10492-009-0018-4/

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