Equilibrated residual method for estimation of modelling and approximation errors in complex piezoelectric models

• Autorzy: Zielińska Magdalena , Zboiński Grzegorz

Identyfikatory

DOI

10.24425/bpasts.2025.153228

• Języki publikacji: EN

Abstrakty

EN

The article presents the equilibrated residual method (ERM) of error estimation in coupled problems in the case of complex piezoelectric models. These models include hierarchical, first-order, and transition models within the mechanical field of displacements, as well as hierarchical models within the electric field of potential. Three (classical, modified and enhanced) transition models are considered. The paper presents a variational formulation of the model problem of general piezoelectricity in the case of complex piezoelectric models and the finite element approximation of this problem. Next, the equilibration residual method for coupled problems of piezoelectricity and complex piezoelectric models is presented. The mechanical, electric and coupled parts of the modelling, approximation and total error estimators, and true errors are given. Effectivity indices (the ratio of estimated error to true error) are used to assess the quality of error estimation in the case of three error parts and three types of error for the complex models of piezoelectric plates. The effectivity results for simple piezoelectric models and uncoupled problems of elasticity and dielectricity are applied as references.

Słowa kluczowe

EN

piezoelectricity; complex models; finite element method; error estimation; equilibrated residual method; ERM; FEM

PL

piezoelektryczność; modele złożone; metoda elementów skończonych; szacowanie błędów; ERM; MES

• Wydawca: Polska Akademia Nauk, Wydział IV Nauk Technicznych
• Czasopismo: Bulletin of the Polish Academy of Sciences. Technical Sciences
• Rocznik: 2025
• Tom: Vol. 73, nr 2
• Strony: art. no. e153228
• Opis fizyczny: Bibliogr. 23 poz., rys., tab.

Twórcy

autor

Zielińska Magdalena

• Faculty of Technical Sciences, University of Warmia and Mazury in Olsztyn, Poland

• https://orcid.org/0000-0002-8702-6558

autor

Zboiński Grzegorz

• Institute of Fluid-Flow Machinery, Polish Academy of Sciences in Gdansk, Poland

• https://orcid.org/0000-0001-7775-2436

Bibliografia

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Uwagi

Opracowanie rekordu ze środków MNiSW, umowa nr POPUL/SP/0154/2024/02 w ramach programu "Społeczna odpowiedzialność nauki II" - moduł: Popularyzacja nauki (2025).