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http://dx.doi.org/10.12941/jksiam.2020.24.143

A CONSISTENT DISCONTINUOUS BUBBLE SCHEME FOR ELLIPTIC PROBLEMS WITH INTERFACE JUMPS  

KWONG, IN (SAMSUNG ELECTRONICS SEMICONDUCTOR R & D CENTER)
JO, WANGHYUN (DEPARTMENT OF MATHEMATICS, KUNSAN NATIONAL UNIVERSITY)
Publication Information
Journal of the Korean Society for Industrial and Applied Mathematics / v.24, no.2, 2020 , pp. 143-159 More about this Journal
Abstract
We propose a consistent numerical method for elliptic interface problems with nonhomogeneous jumps. We modify the discontinuous bubble immersed finite element method (DB-IFEM) introduced in (Chang et al. 2011), by adding a consistency term to the bilinear form. We prove optimal error estimates in L2 and energy like norm for this new scheme. One of the important technique in this proof is the Bramble-Hilbert type of interpolation error estimate for discontinuous functions. We believe this is a first time to deal with interpolation error estimate for discontinuous functions. Numerical examples with various interfaces are provided. We observe optimal convergence rates for all the examples, while the performance of early DB-IFEM deteriorates for some examples. Thus, the modification of the bilinear form is meaningful to enhance the performance.
Keywords
Discontinuous bubble scheme; immersed finite element method; elliptic equation with interface; nonhomogeneous-jump condition; structured grids;
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