A Discontinuous Galerkin Method by Patch Reconstruction for Biharmonic Problem
This work provides a novel numerical method for solving biharmonic problems, which are important in engineering and physics, but the contribution is incremental as it extends existing DG techniques.
The authors propose a new discontinuous Galerkin method using least-squares patch reconstruction for solving the biharmonic problem, proving optimal error estimates and demonstrating accuracy and efficiency through 2D and 3D numerical examples on various meshes.
We propose a new discontinuous Galerkin method based on the least-squares patch reconstruction for the biharmonic problem. We prove the optimal error estimate of the proposed method. The two-dimensional and three-dimensional numerical examples are presented to confirm the accuracy and efficiency of the method with several boundary conditions and several types of polygon meshes and polyhedral meshes.