Abstract
AbstractIn this paper, we propose a robust multigrid method for 1D immersed finite element method (IFEM). It is shown that the multigrid method is optimal, which means that the convergence rate of the multigrid method is not only independent of the mesh size h and mesh level L, but also independent of the jump of the discontinuous coefficients. Although we only consider 1D interface method, to the best of our knowledge, this is the first attempt to give a rigorous theoretical analysis for the multigrid method for the IFEM. On the way to this goal, we also revisit the IFEM for the 1D interface problem and prove that the error estimates with respect to the L2 norm and weighted H1 semi‐norm are optimal and independent of the jump of the discontinuous coefficients. Numerical results are given to verify our theoretical findings.
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