# Convergence results with natural norms: Stabilized Lagrange multiplier method for elliptic interface problems

## TL;DR

This paper introduces a stabilized Lagrange multiplier method for elliptic interface problems that relaxes traditional stability conditions and achieves optimal, mesh-independent convergence, supported by numerical validation.

## Contribution

It presents a novel stabilized mortar method that alleviates LBB condition requirements through penalty terms, ensuring optimal convergence in natural, mesh-independent norms.

## Key findings

- Optimal convergence in natural norm
- Method alleviates LBB condition
- Numerical experiments confirm theoretical results

## Abstract

A stabilized Lagrange multiplier method for second order elliptic interface problems is presented in the framework of mortar method. The requirement of LBB (Ladyzhenskaya-Babu\v{s}ka-Brezzi) condition for mortar method is alleviated by introducing penalty terms in the formulation. Optimal convergence results are established in natural norm which is independent of mesh. Numerical experiments are conducted in support of the theoretical derivations.