Numerical analysis of curved C1-finite element methods: applications tothin-plate and thin-shell problems,

摘要

Abstract: Thin plate and thin shell problems are generally set on plane reference domains with a curved boundary. Their approximation by conforming finite element methods requires C$+1$/- curved finite elements entirely compatible with the associated C$+1$/-rectilinear finite elements. In this contribution, we introduce a C$+1$/-curved finite element compatible with the P$-5$/-Argyris element, we study its approximation properties, and then, we use such an element to approximate the solution of thin plate or thin shell problems set on a plane curved boundary domain. Finally, we discuss the use of such C$+1$/-curved elements to approximate junctions between thin shells.!29