Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely: The ighted essentially non-oscillatory (WENO) methods are a popular high-order spatial discretization for hyperbolic partial differential equations. Typical treatments of WENO methods assume a uniform mesh. ,  give explicit formulas for the finite-volume, fifth-order WENO (WENO5) method on non-uniform meshes in a way that is amenable to efficient implementation.  then compare the performance of the non-uniform mesh approach with the classical uniform mesh approach for the finite-volume formulation of the WENO5 method.  find that the numerical results significantly favor the non-uniform mesh approach both in terms of computational efficiency as ll as memory usage.  expect this investigation to provide a basis for future work on adaptive mesh methods coupled with the finite-volume WENO methods.
['Rong Wang', 'Hui Feng', 'Raymond J. Spiteri']
I am writing a research paper on a idea Observations on the fifth-order WENO method with non-uniform meshes
[{"from": "human", "value": "I am writing a research paper on a idea Observations on the fifth-order WENO method with non-uniform meshes"}, {"from": "gpt", "value": "Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely: The ighted essentially non-oscillatory (WENO) methods are a popular high-order spatial discretization for hyperbolic partial differential equations. Typical treatments of WENO methods assume a uniform mesh. ,  give explicit formulas for the finite-volume, fifth-order WENO (WENO5) method on non-uniform meshes in a way that is amenable to efficient implementation.  then compare the performance of the non-uniform mesh approach with the classical uniform mesh approach for the finite-volume formulation of the WENO5 method.  find that the numerical results significantly favor the non-uniform mesh approach both in terms of computational efficiency as ll as memory usage.  expect this investigation to provide a basis for future work on adaptive mesh methods coupled with the finite-volume WENO methods."}]