A posteriori finite element output bounds in three space dimensions using the FETI method Original Research Article

A domain decomposition finite element technique for efficiently generating lower and upper bounds to outputs which are linear functionals of the solution to the convection–diffusion equation is presented. The novelty is to utilize a domain decomposition method with Lagrange multipliers and an iterative interface solution scheme – the finite element tearing and interconnecting (FETI) procedure – to extend the bound method to three space dimensions. Numerical results show that the bounds are sharp, their calculation consumes only a fraction of the memory required by a sparse solver, and CPU usage is optimal, i.e. proportional to the total number of d.o.f.