A fully discrete stabilized mixed finite volume element formulation for the non-stationary conduction-convection problem

作者：Luo, Zhendong^*; Li, Hong; Sun, Ping

来源：Journal of Mathematical Analysis and Applications, 2013, 404(1): 71-85.

DOI：10.1016/j.jmaa.2013.03.001

• Non-stationary conduction-convection problem
• Stabilized mixed finite volume element formulation
• Local Gauss integrals and parameter-free
• Error estimate

At first, a semi-discrete formulation with respect to time for the non-stationary conduction-convection problem is recalled. Then, a fully discrete stabilized mixed finite volume element (SMFVE) formulation based on two local Gauss integrals and parameter-free is established directly from the semi-discrete formulation with respect to time for the non-stationary conduction-convection problem. Following this, the error estimates for the fully discrete SMFVE solutions are derived by means of the standard mixed finite element method. Finally, some numerical experiments are presented illustrating that the numerical errors are consistent with theoretical results, the degrees of freedom of the fully discrete SMFVE formulation are far fewer than those of the classical finite volume element (FVE) formulation without any stabilization, and its numerical solutions are more stable than those of the classical EVE formulation without any stabilization, thus validating that the fully discrete SMFVE formulation is feasible and efficient for finding the numerical solutions of the non-stationary conduction-convection problem.

• 出版日期2013-8-1
• 单位贵州师范大学; 华北电力大学; 华北电力大学（保定）; 内蒙古大学