Discontinuous Galerkin Finite Element Methods for 1D Rosenau Equation

TL;DR

This paper develops and analyzes discontinuous Galerkin finite element methods for the 1D Rosenau equation, providing theoretical guarantees and numerical validation of accuracy, stability, and decay properties.

Contribution

The paper introduces a novel application of discontinuous Galerkin methods to the Rosenau equation with rigorous theoretical analysis and numerical validation.

Findings

Optimal error estimates established for the schemes

Numerical results confirm decay estimates and theoretical predictions

The methods demonstrate stability and accuracy for the Rosenau equation

Abstract

In this paper, discontinuous Galerkin finite element methods are applied to one dimensional Rosenau equation. Theoretical results including consistency, a priori bounds and optimal error estimates are established for both semidiscrete and fully discrete schemes. Numerical experiments are performed to validate the theoretical results. The decay estimates are verified numerically for the Rosenau equation.