DPG method with optimal test functions for a transmission problem

TL;DR

This paper introduces a DPG method with optimal test functions for elliptic transmission problems, combining boundary integral operators and ultra-weak formulations to achieve quasi-optimal approximation and confirm optimal convergence through numerical experiments.

Contribution

It presents a novel DPG approach with optimal test functions for transmission problems, ensuring stability and optimal convergence.

Findings

Principal unknowns are approximated quasi-optimally.

Numerical experiments confirm optimal convergence orders.

Method effectively handles smooth and singular solutions.

Abstract

We propose and analyze a numerical method to solve an elliptic transmission problem in full space. The method consists of a variational formulation involving standard boundary integral operators on the coupling interface and an ultra-weak formulation in the interior. To guarantee the discrete inf-sup condition, the system is discretized by the DPG method with optimal test functions. We prove that principal unknowns are approximated quasi-optimally. Numerical experiments for problems with smooth and singular solutions confirm optimal convergence orders.