{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,3,26]],"date-time":"2025-03-26T08:43:08Z","timestamp":1742978588195,"version":"3.40.3"},"publisher-location":"Cham","reference-count":10,"publisher":"Springer International Publishing","isbn-type":[{"type":"print","value":"9783030558734"},{"type":"electronic","value":"9783030558741"}],"license":[{"start":{"date-parts":[[2020,8,22]],"date-time":"2020-08-22T00:00:00Z","timestamp":1598054400000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springer.com\/tdm"},{"start":{"date-parts":[[2020,8,22]],"date-time":"2020-08-22T00:00:00Z","timestamp":1598054400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.springer.com\/tdm"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2021]]},"DOI":"10.1007\/978-3-030-55874-1_117","type":"book-chapter","created":{"date-parts":[[2021,5,3]],"date-time":"2021-05-03T11:52:51Z","timestamp":1620042771000},"page":"1177-1184","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":3,"title":["Dynamic and Weighted Stabilizations of the L-scheme Applied to a Phase-Field Model for Fracture Propagation"],"prefix":"10.1007","author":[{"given":"Christian","family":"Engwer","sequence":"first","affiliation":[]},{"given":"Iuliu Sorin","family":"Pop","sequence":"additional","affiliation":[]},{"given":"Thomas","family":"Wick","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2020,8,22]]},"reference":[{"key":"117_CR1","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-642-61257-2","volume-title":"Numerical continuation methods: an introduction","author":"E L Allgower","year":"1990","unstructured":"E. L. Allgower and K. Georg. Numerical continuation methods: an introduction. Springer, 1990."},{"key":"117_CR2","doi-asserted-by":"crossref","unstructured":"D. Arndt, W. Bangerth, T. C. Clevenger, D. Davydov, M. Fehling, D. Garcia-Sanchez, G. Harper, T. Heister, L. Heltai, M. Kronbichler, R. M. Kynch, M. Maier, J.-P. Pelteret, B. Turcksin, and D. Wells. The deal.II library, version 9.1. J. Numer. Math., 27(4):203\u2013213, 2019.","DOI":"10.1515\/jnma-2019-0064"},{"key":"117_CR3","doi-asserted-by":"publisher","first-page":"112752","DOI":"10.1016\/j.cma.2019.112752","volume":"361","author":"M K Brun","year":"2020","unstructured":"M. K. Brun, T. Wick, I. Berre, J. M. Nordbotten, and F. A. Radu. An iterative staggered scheme for phase field brittle fracture propagation with stabilizing parameters. Comp. Meth. Appl. Mech. Engrg., 361:112752, 2020.","journal-title":"Comp. Meth. Appl. Mech. Engrg."},{"key":"117_CR4","doi-asserted-by":"publisher","first-page":"276","DOI":"10.1016\/j.cma.2015.12.017","volume":"312","author":"T Gerasimov","year":"2016","unstructured":"T. Gerasimov and L. D. Lorenzis. A line search assisted monolithic approach for phase-field computing of brittle fracture. Comp. Meth. Appl. Mech. Engrg., 312:276\u2013303, 2016.","journal-title":"Comp. Meth. Appl. Mech. Engrg."},{"issue":"2","key":"117_CR5","doi-asserted-by":"publisher","first-page":"341","DOI":"10.1007\/s10596-016-9566-3","volume":"20","author":"F List","year":"2016","unstructured":"F. List and F. A. Radu. A study on iterative methods for solving Richards\u2019 equation. Comput. Geosci., 20(2):341\u2013353, 2016.","journal-title":"Comput. Geosci."},{"key":"117_CR6","doi-asserted-by":"publisher","first-page":"420","DOI":"10.1016\/j.cma.2014.10.052","volume":"290","author":"A Mesgarnejad","year":"2015","unstructured":"A. Mesgarnejad, B. Bourdin, and M. Khonsari. Validation simulations for the variational approach to fracture. Comp. Meth. Appl. Mech. Engrg., 290:420\u2013437, 2015.","journal-title":"Comp. Meth. Appl. Mech. Engrg."},{"key":"117_CR7","doi-asserted-by":"publisher","first-page":"1273","DOI":"10.1002\/nme.2861","volume":"83","author":"C Miehe","year":"2010","unstructured":"C. Miehe, F. Welschinger, and M. Hofacker. Thermodynamically consistent phase-field models of fracture: variational principles and multi-field FE implementations. Int. J. Numer. Methods Engrg., 83:1273\u20131311, 2010.","journal-title":"Int. J. Numer. Methods Engrg."},{"issue":"1\u20132","key":"117_CR8","doi-asserted-by":"publisher","first-page":"365","DOI":"10.1016\/j.cam.2003.04.008","volume":"168","author":"I S Pop","year":"2004","unstructured":"I. S. Pop, F. Radu, and P. Knabner. Mixed finite elements for the Richards\u2019 equation: linearization procedure. J. Comput. Appl. Math., 168(1\u20132):365\u2013373, 2004.","journal-title":"J. Comput. Appl. Math."},{"key":"117_CR9","doi-asserted-by":"publisher","first-page":"69","DOI":"10.1016\/j.cma.2013.12.005","volume":"271","author":"M Wheeler","year":"2014","unstructured":"M. Wheeler, T. Wick, and W. Wollner. An augmented-Lagangrian method for the phase-field approach for pressurized fractures. Comp. Meth. Appl. Mech. Engrg., 271:69\u201385, 2014.","journal-title":"Comp. Meth. Appl. Mech. Engrg."},{"issue":"4","key":"117_CR10","doi-asserted-by":"publisher","first-page":"B589","DOI":"10.1137\/16M1063873","volume":"39","author":"T Wick","year":"2017","unstructured":"T. Wick. An error-oriented Newton\/inexact augmented Lagrangian approach for fully monolithic phase-field fracture propagation. SIAM J. Sci. Comput., 39(4):B589\u2013B617, 2017.","journal-title":"SIAM J. Sci. Comput."}],"container-title":["Lecture Notes in Computational Science and Engineering","Numerical Mathematics and Advanced Applications ENUMATH 2019"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/978-3-030-55874-1_117","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2022,5,6]],"date-time":"2022-05-06T00:15:32Z","timestamp":1651796132000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/978-3-030-55874-1_117"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2020,8,22]]},"ISBN":["9783030558734","9783030558741"],"references-count":10,"URL":"https:\/\/doi.org\/10.1007\/978-3-030-55874-1_117","relation":{},"ISSN":["1439-7358","2197-7100"],"issn-type":[{"type":"print","value":"1439-7358"},{"type":"electronic","value":"2197-7100"}],"subject":[],"published":{"date-parts":[[2020,8,22]]},"assertion":[{"value":"22 August 2020","order":1,"name":"first_online","label":"First Online","group":{"name":"ChapterHistory","label":"Chapter History"}}]}}