A new Cement to Glue non-conforming Grids with Robin interface conditions: the finite element case
This work addresses the challenge of coupling non-conforming grids in finite element methods, which is important for computational mechanics and multiphysics simulations.
The paper introduces a new domain decomposition method for non-conforming grids using Robin interface conditions, proving well-posedness and convergence of the iterative solver, with error analysis for 2D low/high-order polynomials and 3D P1 elements, supported by 2D numerical results.
We design and analyze a new non-conforming domain decomposition method based on Schwarz type approaches that allows for the use of Robin interface conditions on non-conforming grids. The method is proven to be well posed, and the iterative solver to converge. The error analysis is performed in 2D piecewise polynomials of low and high order and extended in 3D for $P_1$ elements. Numerical results in 2D illustrate the new method.