A Raviart–Thomas mixed finite element scheme for the two‐dimensional three‐temperature heat conduction problems

• Published in: International journal for numerical methods in engineering Vol. 111; no. 10; pp. 983 - 1000
• Main Authors: Nie, Cunyun, Yu, Haiyuan
• Format: Journal Article
• Language: English
• Published: Chichester, UK John Wiley & Sons, Ltd 07.09.2017; Wiley Subscription Services, Inc
• Subjects: 2D 3‐T radiative heat conduction problem; Center of gravity; Conduction heating; Conductive heat transfer; Convergence; error estimates; Finite element method; Flux; Freezing; Heat; Mathematical analysis; Nonlinear equations; Raviart–Thomas mixed finite element scheme; Robustness (mathematics); small energy conservative error; Triangulation
• ISSN: 0029-5981; 1097-0207
• DOI: 10.1002/nme.5492

Summary For the two‐dimensional three‐temperature radiative heat conduction problem appearing in the inertial confinement numerical stimulations, we choose the Freezing coefficient method to linearize the nonlinear equations, and initially apply the well‐known mixed finite element scheme with the lowest order Raviart–Thomas element associated with the triangulation to the linearized equations, and obtain the convergence with one order with respect to the space direction for the temperature and flux function approximations, and design a simple but efficient algorithm for the discrete system. Three numerical examples are displayed. The former two verify theoretical results and show the super‐convergence for temperature and flux functions at the barycenter of the element, which is helpful for solving the radiative heat conduction problems. The third validates the robustness of this scheme with small energy conservative error and one order convergence for the time discretization. Copyright © 2016 John Wiley & Sons, Ltd.