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Using a C\u00e9a-type lemma, a supercloseness result, and a non-standard duality argument, we prove <jats:inline-formula><jats:alternatives><jats:tex-math>$$W^{1,p}(\\varOmega )$$<\/jats:tex-math><mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n                  <mml:mrow>\n                    <mml:msup>\n                      <mml:mi>W<\/mml:mi>\n                      <mml:mrow>\n                        <mml:mn>1<\/mml:mn>\n                        <mml:mo>,<\/mml:mo>\n                        <mml:mi>p<\/mml:mi>\n                      <\/mml:mrow>\n                    <\/mml:msup>\n                    <mml:mrow>\n                      <mml:mo>(<\/mml:mo>\n                      <mml:mi>\u03a9<\/mml:mi>\n                      <mml:mo>)<\/mml:mo>\n                    <\/mml:mrow>\n                  <\/mml:mrow>\n                <\/mml:math><\/jats:alternatives><\/jats:inline-formula>-, <jats:inline-formula><jats:alternatives><jats:tex-math>$$L^\\infty (\\varOmega )$$<\/jats:tex-math><mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n                  <mml:mrow>\n                    <mml:msup>\n                      <mml:mi>L<\/mml:mi>\n                      <mml:mi>\u221e<\/mml:mi>\n                    <\/mml:msup>\n                    <mml:mrow>\n                      <mml:mo>(<\/mml:mo>\n                      <mml:mi>\u03a9<\/mml:mi>\n                      <mml:mo>)<\/mml:mo>\n                    <\/mml:mrow>\n                  <\/mml:mrow>\n                <\/mml:math><\/jats:alternatives><\/jats:inline-formula>-, <jats:inline-formula><jats:alternatives><jats:tex-math>$$W^{1,\\infty }(\\varOmega )$$<\/jats:tex-math><mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n                  <mml:mrow>\n                    <mml:msup>\n                      <mml:mi>W<\/mml:mi>\n                      <mml:mrow>\n                        <mml:mn>1<\/mml:mn>\n                        <mml:mo>,<\/mml:mo>\n                        <mml:mi>\u221e<\/mml:mi>\n                      <\/mml:mrow>\n                    <\/mml:msup>\n                    <mml:mrow>\n                      <mml:mo>(<\/mml:mo>\n                      <mml:mi>\u03a9<\/mml:mi>\n                      <mml:mo>)<\/mml:mo>\n                    <\/mml:mrow>\n                  <\/mml:mrow>\n                <\/mml:math><\/jats:alternatives><\/jats:inline-formula>-, and <jats:inline-formula><jats:alternatives><jats:tex-math>$$H^{1\/2}(\\partial \\varOmega )$$<\/jats:tex-math><mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n                  <mml:mrow>\n                    <mml:msup>\n                      <mml:mi>H<\/mml:mi>\n                      <mml:mrow>\n                        <mml:mn>1<\/mml:mn>\n                        <mml:mo>\/<\/mml:mo>\n                        <mml:mn>2<\/mml:mn>\n                      <\/mml:mrow>\n                    <\/mml:msup>\n                    <mml:mrow>\n                      <mml:mo>(<\/mml:mo>\n                      <mml:mi>\u2202<\/mml:mi>\n                      <mml:mi>\u03a9<\/mml:mi>\n                      <mml:mo>)<\/mml:mo>\n                    <\/mml:mrow>\n                  <\/mml:mrow>\n                <\/mml:math><\/jats:alternatives><\/jats:inline-formula>-error estimates under reasonable assumptions on the regularity of the exact solution and <jats:inline-formula><jats:alternatives><jats:tex-math>$$L^p(\\varOmega )$$<\/jats:tex-math><mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n                  <mml:mrow>\n                    <mml:msup>\n                      <mml:mi>L<\/mml:mi>\n                      <mml:mi>p<\/mml:mi>\n                    <\/mml:msup>\n                    <mml:mrow>\n                      <mml:mo>(<\/mml:mo>\n                      <mml:mi>\u03a9<\/mml:mi>\n                      <mml:mo>)<\/mml:mo>\n                    <\/mml:mrow>\n                  <\/mml:mrow>\n                <\/mml:math><\/jats:alternatives><\/jats:inline-formula>-error estimates under comparatively mild assumptions on the involved contact sets. The obtained orders of convergence turn out to be optimal for problems with essentially bounded right-hand sides. Our results are accompanied by numerical experiments which confirm the theoretical findings.<\/jats:p>","DOI":"10.1007\/s00211-020-01117-z","type":"journal-article","created":{"date-parts":[[2020,5,26]],"date-time":"2020-05-26T21:04:25Z","timestamp":1590527065000},"page":"513-551","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":7,"title":["Finite element error estimates in non-energy norms for the two-dimensional scalar Signorini problem"],"prefix":"10.1007","volume":"145","author":[{"given":"Constantin","family":"Christof","sequence":"first","affiliation":[]},{"given":"Christof","family":"Haubner","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2020,5,26]]},"reference":[{"key":"1117_CR1","volume-title":"Sobolev Spaces","author":"RA Adams","year":"1975","unstructured":"Adams, R.A.: Sobolev Spaces. 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