\(L_ 2\)-error bounds for approximate solutions of elliptic partial differential equations with Dirichlet-boundary conditions (Q1262718)

Let u be the exact solution of the boundary value problem \(Au:=- D(pDu)+qu=f,\quad x\in G\) and \(u=0,\quad x\in \partial G,\) v being any approximation of it; D is the vector of partial derivatives with respect to the components of x. New a posteriori computable error bounds for the \(L_ 2\)-norms, both of \(D(u-v)\) and \(u-v\) are proposed. It is shown that the new error bounds are better than the classical ones.