Parallel least-squares finite element method for time-dependent convection-diffusion system (Q644841)

The authors consider the convection-diffusion equation in one space dimension. The equation is rewritten as a first order system in space. For the time discretization the backward Euler method is used and for the spatial discretization least-squares finite elements with piecewise polynomials (of possible different degree for each of the two solution components). The space interval is decomposed in overlapping subintervals and a corresponding parallel domain decomposition algorithm is set up for which an a priori error estimate is proved as main result of the paper. There is a longer section with numerical experiments, also for an equation with a square in \(\mathbb{R}^2\) as domain.