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A partially penalized P 1 / CR immersed finite element method for planar elasticity interface problems
Author(s) -
Liu Angran,
Chen Jinru
Publication year - 2019
Publication title -
numerical methods for partial differential equations
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.901
H-Index - 61
eISSN - 1098-2426
pISSN - 0749-159X
DOI - 10.1002/num.22416
Subject(s) - mathematics , finite element method , elasticity (physics) , planar , norm (philosophy) , mathematical analysis , degrees of freedom (physics and chemistry) , geometry , physics , thermodynamics , computer graphics (images) , computer science , political science , law
Abstract We propose a partially penalized P 1 / CR immersed finite element (IFE) method with midpoint values on edges as degrees of freedom for CR elements to solve planar elasticity interface problems. Optimal approximation errors in L 2 norm and H 1 semi‐norm are obtained for the P 1 / CR IFE spaces. Moreover, by adding some stabilization terms on the edges of interface elements, we derive an optimal error estimate for the P 1 / CR IFE method. Our method differs from the method with average values on edges as degrees of freedom for P 1 / CR elements in Qin et al.'s study, where no approximation theoretical result was presented. Numerical examples confirm our theoretical results.