A new Cement to Glue non-conforming Grids with Robin interface conditions: the finite element case

TL;DR

This paper introduces a novel non-conforming domain decomposition method utilizing Robin interface conditions, proven to be well-posed and convergent, with error analysis and numerical validation in 2D and 3D.

Contribution

It presents a new Schwarz-type method for non-conforming grids with Robin conditions, including theoretical analysis and numerical experiments.

Findings

Method is well-posed and convergent.

Error analysis extends to 3D for P1 elements.

Numerical results validate the approach.

Abstract

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.