Dolzmann, Georg Optimal convergence for the finite element method in Campanato spaces. (English) Zbl 0929.65096 Math. Comput. 68, No. 228, 1397-1427 (1999). The author proves a priori estimates and optimal error estimates for linear finite element approximations of elliptic systems in divergence form with continuous coefficients in Campanato spaces. The proofs rely on discrete analogues of the Campanato inequalities for the solution of the system, which locally measure the decay of the energy. Using this results, the author gives a new proof of the well-known \(\mathring W^1_\infty\)-results of R. Rannacher and R. Scott [ibid. 38, 437-445 (1982; Zbl 0483.65007)]. Reviewer: Ziwen Jiang (Shandong) Cited in 5 Documents MSC: 65N15 Error bounds for boundary value problems involving PDEs 65N12 Stability and convergence of numerical methods for boundary value problems involving PDEs 35J25 Boundary value problems for second-order elliptic equations 65N30 Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs Keywords:optimal error estimates; finite element methods; Campanato spaces; elliptic systems Citations:Zbl 0483.65007 PDFBibTeX XMLCite \textit{G. Dolzmann}, Math. Comput. 68, No. 228, 1397--1427 (1999; Zbl 0929.65096) Full Text: DOI