Finite element approximations of parametrized strongly nonlinear boundary value problems. (Q1859348)

The author presents a theory of a priori error estimates of the finite element solution of the boundary value problem \[ F(\lambda, u)= 0,\quad (\lambda, u)\in\Lambda\times W^{-1,P}_0(\Omega). \] In section 2 a finite-dimensional approximation of this problem in an abstract Banach space is considered. The applicability of the formulas of a priori error estimates \[ \| u(\lambda)- u_h(\lambda)\leq Ch\| u(\lambda)\| \] is difficult in practical calculation.