{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,5,14]],"date-time":"2025-05-14T04:47:44Z","timestamp":1747198064162,"version":"3.40.5"},"reference-count":26,"publisher":"Walter de Gruyter GmbH","issue":"2","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2025,4,1]]},"abstract":"<jats:title>Abstract<\/jats:title>\n               <jats:p>We consider nodal-based Lagrangian interpolations for the finite element approximation of the Maxwell eigenvalue problem. The first approach introduced is a standard Galerkin method on Powell\u2013Sabin meshes, which has recently been shown to yield convergent approximations in two dimensions, whereas the other two are stabilized formulations that can be motivated by a variational multiscale approach. For the latter, a mixed formulation equivalent to the original problem is used, in which the operator has a saddle point structure. The Lagrange multiplier introduced to enforce the divergence constraint vanishes in an appropriate functional setting. The first stabilized method consists of an augmented formulation including a mesh dependent term that can be regarded as the Laplacian of the divergence constraint multiplier. The second formulation is based on orthogonal projections, which can be recast as a residual based stabilization technique. We rely on the classical spectral theory to analyze the approximating methods for the eigenproblem. The stability and convergence aspects are inherited from the associated source problems together with an assumption which is discussed numerically. We investigate the performance of the proposed formulations and provide some convergence results validating the theoretical ones for several benchmark tests, including ones with smooth and singular solutions.<\/jats:p>","DOI":"10.1515\/cmam-2023-0081","type":"journal-article","created":{"date-parts":[[2024,10,1]],"date-time":"2024-10-01T17:00:48Z","timestamp":1727802048000},"page":"349-371","source":"Crossref","is-referenced-by-count":0,"title":["Finite Element Formulations for Maxwell\u2019s Eigenvalue Problem Using Continuous Lagrangian Interpolations"],"prefix":"10.1515","volume":"25","author":[{"given":"Daniele","family":"Boffi","sequence":"first","affiliation":[{"name":"King Abdullah University of Science and Technology , Thuwal 23955-6900 , Saudi Arabia ; and University of Pavia, Pavia 27100, Italy"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Ramon","family":"Codina","sequence":"additional","affiliation":[{"name":"Universitat Polit\u00e8cnica de Catalunya ; and International Centre for Numerical Methods in Engineering (CIMNE), 08034 Barcelona , Spain"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-9609-1888","authenticated-orcid":false,"given":"\u00d6nder","family":"T\u00fcrk","sequence":"additional","affiliation":[{"name":"Institute of Applied Mathematics , 52984 Middle East Technical University , 06800 Ankara , T\u00fcrkiye"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"374","published-online":{"date-parts":[[2024,10,2]]},"reference":[{"key":"2025032910202875204_j_cmam-2023-0081_ref_001","doi-asserted-by":"crossref","unstructured":"C.  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