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This article introduces a new primal-dual weak Galerkin (PDWG) finite elementmethod for second order elliptic interface problems with ultra-low regularityassumptions on the exact solution and the interface and boundary data. It isproved that the PDWG method is stable and accurate with optimal order of errorestimates in discrete and Sobolev norms. In particular, the error estimates arederived under the low regularity assumption of $u\in H^{\delta}(\Omega)$ for$\delta > \frac12$ for the exact solution $u$. Extensive numerical experimentsare conducted to provide numerical solutions that verify the efficiency andaccuracy of the new PDWG method.

A New Primal-Dual Weak Galerkin Method for Elliptic Interface Problems with Low Regularity Assumptions