Work

A novel penalty-based least-squares discontinuous Galerkin (LS-DG) method for time-dependent Stokes equations

Year: 2026

Type: article

Abstract: In this paper, a new penalty-based least-squares discontinuous Galerkin (LS-DG) framework is proposed and analyzed for the time-dependent Stokes system. A key feature of the scheme is the use of a penalty method to address the incompressibility constraint, along with the introduction of an artificial average perturbation term in the weighted least-squares functional. This approach offers three distinct advantages: first, it facilitates the proof of coercivity of the functional, ensuring the unique solvability of the method; second, it guarantees the unconditional stability of the kinetic energy at the discrete level; and third, it integrates the strengths of both the discontinuous Galerkin and least-squares methods, naturally providing a built-in residual indicator for the adaptive procedure. We rigorously establish the well-posedness and derive optimal error estimates for the proposed scheme. Finally, the accuracy, energy stability, and high efficiency of the method are demonstrated through several numerical examples, which show that it outperforms the classical DG method in terms of computational efficiency.

Source: Advances in Computational Mathematics

DOI: 10.1007/s10444-026-10349-w

Authors: Guang-an Zou, Kejia Pan, Xiaofeng Yang

Institutions: Henan University, Central South University, University of South Carolina

Language: English

Topic: Advanced Numerical Methods in Computational Mathematics

Subfield: Computational Mechanics

Field: Engineering

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $3,190

Funders: National Science Foundation, Natural Science Foundation of Henan Province