Finite element approximation for some quasilinear elliptic problems
The authors consider the finite element approximation of the boundary value problem \[ -\nabla\cdot(A(u)\nabla u) = f \quad \text{in } \Omega, \qquad u = 0 \quad \text{on } \partial\Omega. \] where \(\Omega\) is a two- or three-dimensional polyhedral domain and \(A(u)\) is a Lipschitz continuous function satisfying \(A(u)\geq\delta>0\). Under the assumption of the uniqueness of the weak solution, the authors can show the \(L^\infty\) convergence of the approximate solution.
quasilinear elliptic boundary value problem
scientific article; zbMATH DE number 1326428