000145352 001__ 145352 000145352 005__ 20241024135330.0 000145352 0247_ $$2doi$$a10.1109/ACCESS.2024.3443058 000145352 0248_ $$2sideral$$a140116 000145352 037__ $$aART-2024-140116 000145352 041__ $$aeng 000145352 100__ $$ade Curtò, J. 000145352 245__ $$aIsomorphic Structures and Operator Analysis in Mimetic Discretizations 000145352 260__ $$c2024 000145352 5060_ $$aAccess copy available to the general public$$fUnrestricted 000145352 5203_ $$aThis study presents a comprehensive examination of the structural and operatorial foundations within mimetic discretizations, with a focus on bridging the gap between discrete and continuous function spaces. By scrutinizing the mimetic gradient and divergence operators—central to the discretization of the NAVIER-STOKES equations—we study their kernel and image spaces, establishing their isomorphisms through rigorous mathematical proofs. Our methodology leverages discrete scalar and vector function spaces, delineated by grid spacing, to define linear mappings that unveil the subspace relationships and quotient space structures integral to understanding these operators’ roles in computational fluid dynamics. Central to our findings is the application of the first isomorphism theorem, which facilitates a deeper insight into how mimetic discretizations reflect the continuous properties of differential operators within a discrete framework. This allows for an exploration into the algebraic and topological implications of such discretizations, notably in the context of the NAVIER-STOKES equations. Furthermore, we extend our investigation to encompass subalgebras, ideals, their quotients, and the formulation of short exact sequences that mirror the continuous interplay between gradient, divergence, and LAPLACIAN operators. Significant advances include the application of the first isomorphism theorem which confirms that our mimetic discretizations preserve key properties of differential operators, thus enhancing the accuracy and reliability of computational models. Additionally, our research introduces practical extensions into subalgebras and complex operator sequences, laying groundwork for future developments in numerical methods aimed at improving the precision of engineering simulations. 000145352 540__ $$9info:eu-repo/semantics/openAccess$$aby$$uhttp://creativecommons.org/licenses/by/3.0/es/ 000145352 655_4 $$ainfo:eu-repo/semantics/article$$vinfo:eu-repo/semantics/publishedVersion 000145352 700__ $$0(orcid)0000-0002-5844-7871$$ade Zarzà, I.$$uUniversidad de Zaragoza 000145352 7102_ $$15007$$2570$$aUniversidad de Zaragoza$$bDpto. Informát.Ingenie.Sistms.$$cÁrea Lenguajes y Sistemas Inf. 000145352 773__ $$g12 (2024), 112482-112498$$pIEEE Access$$tIEEE Access$$x2169-3536 000145352 8564_ $$s763332$$uhttps://zaguan.unizar.es/record/145352/files/texto_completo.pdf$$yVersión publicada 000145352 8564_ $$s2633815$$uhttps://zaguan.unizar.es/record/145352/files/texto_completo.jpg?subformat=icon$$xicon$$yVersión publicada 000145352 909CO $$ooai:zaguan.unizar.es:145352$$particulos$$pdriver 000145352 951__ $$a2024-10-24-12:11:02 000145352 980__ $$aARTICLE