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For any <jats:inline-formula><jats:alternatives><jats:tex-math>$$\\alpha \\in (1,\\infty )$$<\/jats:tex-math><mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n                  <mml:mrow>\n                    <mml:mi>\u03b1<\/mml:mi>\n                    <mml:mo>\u2208<\/mml:mo>\n                    <mml:mo>(<\/mml:mo>\n                    <mml:mn>1<\/mml:mn>\n                    <mml:mo>,<\/mml:mo>\n                    <mml:mi>\u221e<\/mml:mi>\n                    <mml:mo>)<\/mml:mo>\n                  <\/mml:mrow>\n                <\/mml:math><\/jats:alternatives><\/jats:inline-formula> we prove convergence, including guaranteed convergence rates in the mesh size <jats:italic>h<\/jats:italic> and polynomial degree <jats:italic>p<\/jats:italic> of the FE-solution of the corresponding discrete variational inequality. Moreover, we derive two families of reliable a posteriori error estimators which are applicable to any \u201capproximation\u201d of the exact solution and not only to the FE-solution and can therefore be coupled with an iterative solver. We prove that any quasi-minimizer of those families of a posteriori error estimators satisfies an efficiency estimate. All our results contain known results for the Mosolov problem by setting <jats:inline-formula><jats:alternatives><jats:tex-math>$$\\alpha =2$$<\/jats:tex-math><mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n                  <mml:mrow>\n                    <mml:mi>\u03b1<\/mml:mi>\n                    <mml:mo>=<\/mml:mo>\n                    <mml:mn>2<\/mml:mn>\n                  <\/mml:mrow>\n                <\/mml:math><\/jats:alternatives><\/jats:inline-formula>. Numerical results underline our theoretical findings.<\/jats:p>","DOI":"10.1007\/s00211-024-01433-8","type":"journal-article","created":{"date-parts":[[2024,9,25]],"date-time":"2024-09-25T21:26:33Z","timestamp":1727299593000},"page":"1679-1718","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["hp-FEM for the $$\\alpha $$-Mosolov problem: a priori and a posteriori error estimates"],"prefix":"10.1007","volume":"156","author":[{"given":"Lothar","family":"Banz","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Ernst P.","family":"Stephan","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"297","published-online":{"date-parts":[[2024,9,25]]},"reference":[{"key":"1433_CR1","doi-asserted-by":"publisher","first-page":"351","DOI":"10.1007\/s002110050423","volume":"82","author":"M Ainsworth","year":"1999","unstructured":"Ainsworth, M., Kay, D.: The approximation theory for the p-version finite element method and application to non-linear elliptic PDEs. 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