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This work focuses on investigating its well-posedness and analyzing error estimates for a splitting backward Euler finite element method. We first define a weak solution consistent with the finite element framework. Then, we prove the uniqueness and existence of such a solution using the Galerkin method and derive a priori estimates for high order regularity. Using a splitting technique, we define an splitting approximate solution and analyze its convergence order. Next, we apply N\u00e9d\u00e9lec\u2019s curl-conforming finite elements, Lagrange elements, and the backward Euler method to construct a fully discretized scheme. We demonstrate the stability of the splitting numerical solution and provide error estimates for its convergence order in both temporal and spatial variables. Finally, we present numerical experiments to validate the theoretical results, showing that our method significantly reduces computational complexity compared to the classical finite element method.<\/jats:p>","DOI":"10.1007\/s10915-025-03018-5","type":"journal-article","created":{"date-parts":[[2025,8,15]],"date-time":"2025-08-15T12:32:39Z","timestamp":1755261159000},"update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":2,"title":["Splitting Finite Element Approximations for Quasi-Static Electroporoelasticity Equations"],"prefix":"10.1007","volume":"104","author":[{"given":"Xuan","family":"Liu","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Yongkui","family":"Zou","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Ran","family":"Zhang","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-2310-3435","authenticated-orcid":false,"given":"Yanzhao","family":"Cao","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Amnon J","family":"Meir","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"297","published-online":{"date-parts":[[2025,8,15]]},"reference":[{"issue":"100","key":"3018_CR1","doi-asserted-by":"publisher","first-page":"9","DOI":"10.11588\/ans.2015.100.20553","volume":"3","author":"MS Alnaes","year":"2015","unstructured":"Alnaes, M.S., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C.N., Ring, J., Rognes, M.E., Wells, G.N.: The FEniCS project version 1.5. 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