STABILITY AND ERROR ESTIMATES OF FULLY DISCRETE SCHEMES FOR THE BRUSSELATOR SYSTEM

摘要

Space-time approximations of the Brusselator system of parabolic PDEs are examined. The schemes under consideration are discontinuous (in time) combined with standard conforming finite elements in space. We prove that these schemes inherit the stability estimates of the underlying system of coupled PDEs in the natural energy norms under minimal regularity assumptions. In addition, we prove a priori error estimates of arbitrary order, using a suitable space-time projection, which exhibits best approximation properties. A key feature of this work is that our analysis includes the physical case of different diffusion constants. Computational examples validating our theoretical findings are also presented.