We study adaptive computation of drag-coefficient of flow around a cylinder. We adopt upwind finite element schemes for two-dimensional stationary viscous incompressible Navier-Stokes equations, derive weighted posteriori error estimation for drag-coefficient by introducing a dual problem, and implement adaptive mesh refinement. Numerical examples show feasibility of the scheme and robust performance of estimators.

In this paper a mathematical model for temperature field in deep underground unsteady is developed. We have to deal with two coupled convective-diffusion equations in three dimensional space and we propose a reduced equation, which is a single integro-differential equation, of the coupled system.In order to reduce greatly both the memory requirements and the computational effort, for its numerical approximation our particular concern will be in the treatment of the integral term. We also show some numerical examples.