Published

Adaptive Mesh Refinement and Superconvergence for Two Dimensional Interface Problems

Huayi Wei, Long Chen, Yunqing Huang and Bin Zheng

SIAM Journal on Scientifical Computing, 36(4), A1478--A1499, 2014.

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ABSTRACT:

 Adaptive mesh refinement and the Borgers algorithm are
combined to generate a body-fitted mesh which can resolve the
interface with fine geometric details. Standard linear finite element
method based on such body-fitted meshes is applied to the elliptic
interface problem and proven to be superclose to the linear
interpolant of the exact solution. Based on this superconvergence
result, a maximal norm error estimate is obtained. The data structure
and meshing algorithms, including local refinement and coarsening, are
very simple. In particular, no tree structure is needed. An efficient
solver for solving the resulting linear algebraic systems is also
developed and shown be robust with respect to both the problem size
and the jump of the diffusion coefficients.