Abstract
We propose a new scheme for elasticity problems having discontinuity in the coefficients. In the previous work (Kwak et al., 2014), the authors suggested a method for solving such problems by finite element method using nonfitted grids. The proposed method is based on theP1-nonconforming finite element methods with stabilizing terms. In this work, we modify the method by adding the consistency terms, so that the estimates of consistency terms are not necessary. We show optimal error estimates inH1and divergence norms under minimal assumptions. Various numerical experiments also show optimal rates of convergence.
Highlights
Linear elasticity equations are important governing equations in continuum mechanics, they describe how solid objects are deformed when external forces are applied on them
We propose a new scheme for elasticity problems having discontinuity in the coefficients
Elasticity interface problems are important in various fields such as solid mechanics, material sciences, and biological sciences
Summary
Linear elasticity equations are important governing equations in continuum mechanics, they describe how solid objects are deformed when external forces are applied on them. The problems involving composite materials lead to the discontinuity in the coefficients of the governing equations In this case, there are two types of numerical methods from the point of view of mesh generation. Using a fixed grid has an obvious advantage that we can use the mesh in the previous time step, in the case when the interface changes over time It is suitable for moving interface problems. Lin et al [9] have suggested a numerical method for solving elasticity problem with an interface using rotated Q1-nonconforming finite element on uniform grids and Kwak et al [10] proved the optimal error estimate for P1-nonconforming finite element on triangular grids under an some extra regularity that the stress component belongs to H2.
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