An upwind finite element method for solving hyperbolic equations

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This analysis demonstrates optimal convergence and stability in hyperbolic equations using a Galerkin-based method, highlighting its effectiveness.

Optimal convergence characteristics were achieved using an upwind stabilization mechanism, enhancing stability with piecewise constant approximations.
Error bounds were rigorously established within both H1 and L2 norms, offering a solid theoretical foundation for the framework.
The stabilized weak Galerkin finite element framework was tested computationally, validating its effectiveness and robustness in multidimensional settings.
The findings suggest that the proposed methodology can reliably address hyperbolic systems, potentially influencing future computational methods.

Hayder Neamah (2025) studied this question.

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This analysis demonstrates optimal convergence and stability in hyperbolic equations using a Galerkin-based method, highlighting its effectiveness.