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Direct error in constitutive equation formulation for inverse heat conduction problem
Author(s) -
Babaniyi Olalekan A.,
Oberai Assad A.,
Barbone Paul E.
Publication year - 2018
Publication title -
international journal for numerical methods in engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.421
H-Index - 168
eISSN - 1097-0207
pISSN - 0029-5981
DOI - 10.1002/nme.5846
Subject(s) - mathematics , discretization , partial differential equation , finite element method , classification of discontinuities , scalar (mathematics) , thermal conduction , compressibility , convection–diffusion equation , mathematical analysis , heat equation , constitutive equation , compressible flow , inverse problem , scalar field , physics , geometry , mechanics , mathematical physics , thermodynamics
Summary We present a mixed numerical formulation that handles discontinuities well for scalar hyperbolic partial differential equations. The formulation is based on a least‐square error in the constitutive equation. It is motivated by scalar inverse diffusion problems with interior data and applies to convection of a passive scalar in a discontinuous compressible flow field. We motivate the need for a mixed formulation by discretizing using an irreducible finite element method and discuss some of the limitations of that approach. We then develop and prove that the mixed formulation is well posed and verify that it works for problems with continuous and discontinuous thermal conductivity distributions.