A Discontinuous Galerkin Method by Patch Reconstruction for Biharmonic Problem

TL;DR

This paper introduces a novel discontinuous Galerkin method utilizing patch reconstruction for solving biharmonic problems, demonstrating optimal error estimates and validated through various numerical experiments in 2D and 3D.

Contribution

The paper presents a new DG method based on least-squares patch reconstruction with proven optimal error estimates for biharmonic problems.

Findings

The method achieves optimal error estimates.

Numerical examples confirm accuracy and efficiency.

Applicable to various boundary conditions and mesh types.

Abstract

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.