Pointwise error estimates for a stabilized Galerkin method: Non-selfadjoint problems (Q1960211)

Pointwise error estimates for a stabilized Galerkin method are provided for second-order non-selfadjoint elliptic partial differential equations. The results extend estimates in a previous paper for the self-adjoint problems. The estimates show a local dependence of the error in the \(W^1_{\infty}\)-norm of the solution \(u\) and weak dependence on the global norm. One tool is the so-called discrete Green's function and another one is the verification that the finite element solution is close to the Ritz projection with respect to the \(L_2\)-norm.