2014/01/20 by Carsten Carstensen, Asha K. Dond, Carstensen, Carsten +5
Engineering · #Advanced Numerical Methods in Computational Mathematics #Numerical methods in engineering #Electromagnetic Simulation and Numerical Methods
paper · pdf · doi:10.48550/arxiv.1401.4810
The state-of-the art proof of a global inf-sup condition on mixed finite element schemes does not allow for an analysis of truly indefinite, second-order linear elliptic PDEs. This paper, therefore, first analyses a nonconforming finite element discretization which converges owing to some a priori L2 error estimates even for reduced regularity on non-convex polygonal domains. An equivalence result of that nonconforming finite element scheme to the mixed finite element method (MFEM) leads to the well-posedness of the discrete solution and to a priori error estimates for the MFEM. The explicit residual-based a posteriori error analysis allows some reliable and efficient error control and motivates some adaptive discretization which improves the empirical convergence rates in three computational benchmarks.