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000171680 0247_ $$2doi$$a10.1007/s44007-026-00211-2
000171680 0248_ $$2sideral$$a149388
000171680 037__ $$aART-2026-149388
000171680 041__ $$aeng
000171680 100__ $$aAsghar, Sabia
000171680 245__ $$aConvergence of the Immersed Interface Method in Linear Elasticity
000171680 260__ $$c2026
000171680 5060_ $$aAccess copy available to the general public$$fUnrestricted
000171680 5203_ $$aWe consider an open, bounded, simply connected (Lipschitz) domain in , which contains a closed polyhedral surface or polygonal contour, referred to as the interface. From this interface, forces are exerted in the normal direction. The forces are continuously distributed over the interface, resulting in an integral expression. This features an important characteristic of the immersed interface method. Since the integral cannot be resolved exactly, one relies on numerical quadrature rules to approximate the integral. Therefore, we consider two different linear elasticity problems with forces over a curve or surface (interface) that is located within the (open) domain of computation: (1) The force is defined by an integral over the interface; (2) The force is defined by a quadrature approximation of the integral over the interface. We prove that the -norm of the difference between the solutions from the two elasticity problems is of the same order as the error of quadrature. The results are demonstrated for both bounded and unbounded domains. The proof that we establish relies on the use of: (i) fundamental solutions for linear elasticity, exhibiting singular behaviors (in particular around points of action) and not being in , and (ii) on the use of singularity removal principle and the Extended Trace Theorem. Convergence is demonstrated in the -norm on curves and manifolds. We show some numerical experiments on the basis of fundamental solutions with a Midpoint quadrature rule in an unbounded and a bounded domain. The numerical experiments confirm our theoretical results. We note that the difference between the interface integral and the quadrature rule over the interface holds for the exact solution in the bulk and not for any discretization carried out in the bulk. Hence, in the numerical finite element-based simulations, the numerical results contain an additional error due to the finite element approach.
000171680 536__ $$9info:eu-repo/grantAgreement/ES/DGA/E24-17R$$9info:eu-repo/grantAgreement/ES/MICIU/PID2022-140108NB-I00
000171680 540__ $$9info:eu-repo/semantics/openAccess$$aby$$uhttps://creativecommons.org/licenses/by/4.0/deed.es
000171680 655_4 $$ainfo:eu-repo/semantics/article$$vinfo:eu-repo/semantics/publishedVersion
000171680 700__ $$aPeng, Qiyao
000171680 700__ $$0(orcid)0000-0002-8117-1674$$aJavierre, Etelvina$$uUniversidad de Zaragoza
000171680 700__ $$aVermolen, Fred
000171680 7102_ $$12005$$2595$$aUniversidad de Zaragoza$$bDpto. Matemática Aplicada$$cÁrea Matemática Aplicada
000171680 773__ $$g5, 2 (2026), 40 [22 pp.]$$pMatematica$$tLa Matematica$$x2730-9657
000171680 8564_ $$s980001$$uhttps://zaguan.unizar.es/record/171680/files/texto_completo.pdf$$yVersión publicada
000171680 8564_ $$s1253063$$uhttps://zaguan.unizar.es/record/171680/files/texto_completo.jpg?subformat=icon$$xicon$$yVersión publicada
000171680 909CO $$ooai:zaguan.unizar.es:171680$$particulos$$pdriver
000171680 951__ $$a2026-05-27-11:26:26
000171680 980__ $$aARTICLE