Parallel domain decomposition procedures of improved D-D type for parabolic problems (Q848534)

The paper deals with a generalization of the domain decomposition procedure for the problem \[ \frac{\partial u}{\partial t}- \nabla \cdot(a \nabla u)+bu=f, \quad \text{in} \quad \Omega \times (0,T], \] \[ \frac{\partial u}{\partial n}=0, \quad \text{on}\quad \partial \Omega \times (0,T], \] \[ u=u_0, \quad \text{in} \quad \Omega \subset R^2, \; \text{at} \quad t=0 \] proposed by \textit{C. N. Dawson} and \textit{T. F. Dupont} [Math. Comput. 58, No.~197, 21--34 (1992; Zbl 0746.65072)]. The author considers a general domain instead of a rectangle and its general decomposition with a net-like structure instead of a stripe of sub-rectangles. A priori error estimates are derived.