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Applications include the stream function vorticity formulation of the incompressible 2D Navier-Stokes equations and the von K\u00e1rm\u00e1n equations with Morley, discontinuous Galerkin, <jats:inline-formula><jats:alternatives><jats:tex-math>$$C^{0}$$<\/jats:tex-math><mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n                  <mml:msup>\n                    <mml:mi>C<\/mml:mi>\n                    <mml:mn>0<\/mml:mn>\n                  <\/mml:msup>\n                <\/mml:math><\/jats:alternatives><\/jats:inline-formula> interior penalty, and weakly over-penalized symmetric interior penalty schemes. The proposed new discretizations consider quasi-optimal smoothers for the source term and smoother-type modifications inside the nonlinear terms.<\/jats:p>","DOI":"10.1007\/s00211-023-01356-w","type":"journal-article","created":{"date-parts":[[2023,6,29]],"date-time":"2023-06-29T14:02:18Z","timestamp":1688047338000},"page":"323-368","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":6,"title":["Unified a priori analysis of four second-order FEM for fourth-order quadratic semilinear problems"],"prefix":"10.1007","volume":"154","author":[{"given":"Carsten","family":"Carstensen","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Neela","family":"Nataraj","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Gopikrishnan C.","family":"Remesan","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Devika","family":"Shylaja","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2023,6,29]]},"reference":[{"key":"1356_CR1","first-page":"214","volume":"37","author":"SC Brenner","year":"2010","unstructured":"Brenner, S.C., Gudi, T., Sung, L.Y.: A weakly over-penalized symmetric interior penalty method for the biharmonic problem. 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