On nonconforming approximations for a class of semilinear problems
ABSTRACT
The a priori and a posteriori error analysis in [1, 3] establishes a unified analysis for different finite element approximations to regular roots of nonlinear partial differential equations with a quadratic nonlinearity. A smoother in the source and nonlinearity enables quasi-best approximations in [3] under a set of hypotheses that guarantees the existence and local uniqueness of a discrete solutions by the Newton-Kantorovich theorem. Related assumptions on some computed approximation close to a regular root allow the reliable and efficient a posteriori error analysis [1] for a general class of rough sources introduced in [2]. Applications include nonconforming discretisations for the von Kármán plate and the stream-vorticity formulation of the stationary Navier-Stokes equations in 2D by the Morley, two versions of discontinuous Galerkin, C0 interior penalty, and WOPSIP methods. The talk presents joint work within the working groups of Prof. C. Carstensen and Prof. N. Nataraj.