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We propose a discontinuous Galerkin(DG) method to approximate the ellipticinterface problem on unfitted mesh using a new approximation space. Theapproximation space is constructed by patch reconstruction with one degree offreedom per element. The optimal error estimates in both L2 norm and DG energynorm are obtained, without the typical constraints for DG method on how theinterface intersects to the elements in the mesh. Other than enjoying theadvantages of DG method, our method may achieve even better efficiency than theconforming finite element method, as illustrated by numerical examples.

A Discontinuous Galerkin Method by Patch Reconstruction for Elliptic Interface Problem on Unfitted Mesh