A posteriori finite element output bounds with adaptive mesh refinement: application to a heat transfer problem in a three-dimensional rectangular duct

摘要

Numerical simulations based on an a posteriori finite element bound method with adaptive mesh refinement are presented for the three-dimensional convection-diffusion equation. The bound method provides relevant, quantitative, inexpensive, and rigorous lower and upper bounds to the output on a very fine discretization ("truth" discretization) at a cost close to the coarse mesh calculation ("working" discretization). To achieve a desired bound gap (i.g., difference between upper and lower bounds) at the lowest cost, an adaptive mesh refinement technique is used to refine the mesh only where needed.