Computational analysis demonstrates improved efficiency and unconditional energy stability in time-dependent Stokes equations, highlighting benefits of a penalty-based formulation.
Key Points
To develop and analyze a novel penalty-based least-squares discontinuous Galerkin framework for accurately simulating the time-dependent Stokes system.
Applied a penalty formulation to enforce the incompressibility constraint alongside an artificial average perturbation term within a weighted least-squares functional.
Derived mathematical proofs for coercivity, unique solvability, well-posedness, and optimal error estimates.
Evaluated performance, discrete kinetic energy stability, and computational speed using benchmark numerical simulations.
Established theoretical well-posedness and proved unconditional kinetic energy stability at the discrete level.
Demonstrated optimal error convergence and superior computational efficiency compared to the classical discontinuous Galerkin method.