{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,5,14]],"date-time":"2025-05-14T04:47:43Z","timestamp":1747198063136,"version":"3.40.5"},"reference-count":36,"publisher":"Walter de Gruyter GmbH","issue":"3","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2024,7,1]]},"abstract":"<jats:title>Abstract<\/jats:title>\n               <jats:p>The ability to deal with complex geometries and to go to higher orders is the main advantage of space-time finite element methods. Therefore, we want to develop a solid background from which we can construct appropriate space-time methods. In this paper, we will treat time as another space direction, which is the main idea of space-time methods. First, we will briefly discuss how exactly the vectorial wave equation is derived from Maxwell\u2019s equations in a space-time structure, taking into account Ohm\u2019s law. Then we will derive a space-time variational formulation for the vectorial wave equation using different trial and test spaces. This paper has two main goals. First, we prove unique solvability for the resulting Galerkin\u2013Petrov variational formulation. Second, we analyze the discrete equivalent of the equation in a tensor product and show conditional stability, i.e., under a CFL condition. Understanding the vectorial wave equation and the corresponding space-time finite element methods is crucial for improving the existing theory of Maxwell\u2019s equations and paves the way to computations of more complicated electromagnetic problems.<\/jats:p>","DOI":"10.1515\/cmam-2023-0079","type":"journal-article","created":{"date-parts":[[2024,6,25]],"date-time":"2024-06-25T18:36:35Z","timestamp":1719340595000},"page":"693-723","source":"Crossref","is-referenced-by-count":0,"title":["Space-Time FEM for the Vectorial Wave Equation under Consideration of Ohm\u2019s Law"],"prefix":"10.1515","volume":"24","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-6441-3686","authenticated-orcid":false,"given":"Julia I.\u2009M.","family":"Hauser","sequence":"first","affiliation":[{"name":"Joanneum Research , Institute for Telecommunications, Navigation and Signal Processing , Graz , Austria"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"374","published-online":{"date-parts":[[2024,6,26]]},"reference":[{"key":"2024070116104861050_j_cmam-2023-0079_ref_001","doi-asserted-by":"crossref","unstructured":"D. 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