A Posteriori Error Estimates of Residual Type for Second Order Quasi-Linear Elliptic PDEs (original) (raw)

We derived a posteriori error estimates for the Dirichlet problem with vanishing boundary for quasi-linear elliptic operator: −∇ • (α(x, ∇u)∇u) = f (x) in Ω ⊂ R 2 , u = 0 on ∂Ω, where Ω is assumed to be a polygonal bounded domain in R 2 , f ∈ L 2 (Ω), and α is a bounded function which satisfies the strictly monotone assumption. We estimated the actual error in the H 1-norm by an indicator η which is composed of L 2norms of the element residual and the jump residual. The main result is divided into two parts; the upper bound and the lower bound for the error. Both of them are accompanied with the data oscillation and the α-approximation term emerged from nonlinearity. The design of the adaptive finite element algorithm were included accordingly.