Carsten Carstensen , David Günther , Hella Rabus
E(v) := ∫_{Ω} φ_{0}(|∇v|) dx - ∫ fv dx for v∈V:=H_{0}^{1}(Ω)
with possibly multiple primal solutions u, but with unique stress σ := φ_{0}(|∇u|) sign ∇u The mixed finite element method is motivated by the smoothness of the stress variable σ ∈ H^{1}_{loc}(Ω;R^{2}) while the primal variables are un-controllable and possibly non-unique. The corresponding nonlinear mixed finite element method is introduced, analysed, and implemented. The striking result of this paper is a sharp a posteriori error estimation in the dual formulation, while the a posteriori error analysis in the primal problem suffers from the reliability-efficiency gap. An empirical comparison of that primal with the new mixed discretisation schemes is intended for uniform and adaptive mesh-refinements.