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Up to now, Newton\u2019s method to solve these equations has been analyzed in finite-dimensional settings only. We analyze the problem in infinite dimensions to gain a new viewpoint. We do that by proving global convergence of the infinite-dimensional Newton\u2019s method with Armijo step sizes to the solution of these equations. We only have to add an arbitrarily small diffusion term for this convergence result. We prove that the additional diffusion term only causes minor differences in the solution compared to the original\n                    <jats:inline-formula>\n                      <jats:alternatives>\n                        <jats:tex-math>$$\\varvec{p}$$<\/jats:tex-math>\n                        <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n                          <mml:mrow>\n                            <mml:mi>p<\/mml:mi>\n                          <\/mml:mrow>\n                        <\/mml:math>\n                      <\/jats:alternatives>\n                    <\/jats:inline-formula>\n                    -Stokes equations under the assumption of some regularity. Finally, we test our algorithms on two experiments: A reformulation of the experiment ISMIP-HOM\n                    <jats:inline-formula>\n                      <jats:alternatives>\n                        <jats:tex-math>$$\\varvec{B}$$<\/jats:tex-math>\n                        <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n                          <mml:mrow>\n                            <mml:mi>B<\/mml:mi>\n                          <\/mml:mrow>\n                        <\/mml:math>\n                      <\/jats:alternatives>\n                    <\/jats:inline-formula>\n                    without sliding and a block with sliding. For the former, the approximation of exact step sizes for the Picard iteration and exact step sizes and Armijo step sizes for Newton\u2019s method are superior in the experiment compared to the Picard iteration. For the latter experiment, Newton\u2019s method with Armijo step sizes needs many iterations until it converges fast to the solution. Thus, Newton\u2019s method with approximately exact step sizes is better than Armijo step sizes in this experiment.\n                  <\/jats:p>","DOI":"10.1007\/s11075-024-01941-6","type":"journal-article","created":{"date-parts":[[2024,9,18]],"date-time":"2024-09-18T09:13:39Z","timestamp":1726650819000},"page":"2011-2038","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["Global convergence of Newton\u2019s method for the regularized p-Stokes equations"],"prefix":"10.1007","volume":"99","author":[{"ORCID":"https:\/\/orcid.org\/0009-0005-0005-9736","authenticated-orcid":false,"given":"Niko","family":"Schmidt","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2024,9,17]]},"reference":[{"issue":"9","key":"1941_CR1","doi-asserted-by":"publisher","first-page":"3753","DOI":"10.5194\/gmd-15-3753-2022","volume":"15","author":"Y Fischler","year":"2022","unstructured":"Fischler, Y., R\u00fcckamp, M., Bischof, C., Aizinger, V., Morlighem, M., Humbert, A.: A scalability study of the ice-sheet and sea-level system model (issm, version 4.18). Geosci. Model Dev. 15(9), 3753\u20133771 (2022). https:\/\/doi.org\/10.5194\/gmd-15-3753-2022","journal-title":"Geosci. Model Dev."},{"issue":"5","key":"1941_CR2","doi-asserted-by":"publisher","first-page":"2710","DOI":"10.1137\/110848694","volume":"45","author":"Q Chen","year":"2013","unstructured":"Chen, Q., Gunzburger, M., Perego, M.: Well-Posedness Results for a Nonlinear Stokes Problem Arising in Glaciology. SIAM J. Math. Anal. 45(5), 2710\u20132733 (2013). https:\/\/doi.org\/10.1137\/110848694","journal-title":"SIAM J. Math. Anal."},{"key":"1941_CR3","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1155\/2011\/164581","volume":"2011","author":"G Jouvet","year":"2011","unstructured":"Jouvet, G., Rappaz, J.: Analysis and finite element approximation of a nonlinear stationary stokes problem arising in glaciology. Adv. Numer. Anal. 2011, 1\u201324 (2011). https:\/\/doi.org\/10.1155\/2011\/164581","journal-title":"Adv. Numer. 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