Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely:  examine the long time error behavior of discontinuous Galerkin spectral element approximations to hyperbolic equations.  show that the choice of numerical flux at interior element boundaries affects the growth rate and asymptotic value of the error. Using the upwind flux, the error reaches the asymptotic value faster, and to a lor value than a central flux gives, especially for low resolution computations. The differences in the error caused by the numerical flux choice decrease as the solution becomes better resolved.
['David A. Kopriva', 'Jan Nordström', 'Gregor Gassner']
I am writing a research paper on a idea Error Boundedness of Discontinuous Galerkin Spectral Element Approximations of Hyperbolic Problems
[{"from": "human", "value": "I am writing a research paper on a idea Error Boundedness of Discontinuous Galerkin Spectral Element Approximations of Hyperbolic Problems"}, {"from": "gpt", "value": "Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely:  examine the long time error behavior of discontinuous Galerkin spectral element approximations to hyperbolic equations.  show that the choice of numerical flux at interior element boundaries affects the growth rate and asymptotic value of the error. Using the upwind flux, the error reaches the asymptotic value faster, and to a lor value than a central flux gives, especially for low resolution computations. The differences in the error caused by the numerical flux choice decrease as the solution becomes better resolved."}]