{"DOI":"10.1093/imanum/drab029","abstract":"Abstract\n We develop a discrete counterpart of the De Giorgi\u2013Nash\u2013Moser theory, which provides uniform H\u00f6lder-norm bounds on continuous piecewise affine finite element approximations of second-order linear elliptic problems of the form $-\\nabla \\cdot (A\\nabla u)=f-\\nabla \\cdot F$ with $A\\in L^\\infty (\\varOmega ; {{\\mathbb{R}}}^{n\\times n})$ a uniformly elliptic matrix-valued function, $f\\in L^{q}(\\varOmega )$, $F\\in L^p(\\varOmega ; {{\\mathbb{R}}}^n)$, with $p> n$ and $q> n/2$, on $A$-nonobtuse shape-regular triangulations, which are not required to be quasi-uniform, of a bounded polyhedral Lipschitz domain $\\varOmega \\subset {{\\mathbb{R}}}^n$.","author":[{"family":"Diening","given":"Lars"},{"family":"Scharle","given":"Toni"},{"family":"S\u00fcli","given":"Endre"}],"id":"unknown","issued":{"date-parts":[[2021,5,12]]},"language":"en","publisher":"Oxford University Press (OUP)","title":"Uniform H\u00f6lder-norm bounds for finite element approximations of second-order elliptic equations","type":"article-journal"}