A posteriori error bounds by “local corrections” using the dual mesh

Some EM field problems can be solved in two different, symmetrical ways, which are “complementary” in the sense that each one corrects some deficiencies of the other. In particular, one obtains error bounds this way. Taking as an example the static conduction problem, the authors propose a geometrical presentation of this theory, which generalizes and symmetrizes the classical but a bit forgotten nowadays “hypercircle” principle. The two complementary problems are independent, but they show how having solved one of them allows one to parallelize the solution of the other, by reducing it to a family of local problems (one for each node of the mesh, to be solved in its immediate neighborhood)