Abstract: A mesh adaptation approach based on Hessian matrix is proposed to solve two-dimensional heat conductione equations with coupled electron,iron and photon temperatures.Three kinds of adaptive mesh and two adaptation methods based on gradient and flux of the photon finite element solution are used. It is shown that the energy conservation error and computation efficiency of the approach are improved.

Key words: laser-driven inertial confinement fusion, two-dimensional three-temperature heat conduction equation, mesh adaptation, Hessian matrix