Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely: ,  establish local error analysis of hybridizable discontinuous Galerkin (HDG) methods for convection-dominated diffusion equation in two types of subdomains away from the layers. The first subdomain is of O ( log ( 1 / h ) h 1 / 2 ) away from the interior layers and of O ( log ( 1 / h ) h ) away from the boundary layers and the second one is of O ( ? ) away from the outflow of the boundary. Our local error bound for the first subdomain can be improved by a factor of log ( 1 / h ) .  use ighted estimates to prove the first result by constructing new ight functions and the inf-sup condition of the bilinear form to prove the second one.
['Yanyi Jin']
I am writing a research paper on a idea Local analysis of HDG methods for convection-dominated diffusion problems
[{"from": "human", "value": "I am writing a research paper on a idea Local analysis of HDG methods for convection-dominated diffusion problems"}, {"from": "gpt", "value": "Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely: ,  establish local error analysis of hybridizable discontinuous Galerkin (HDG) methods for convection-dominated diffusion equation in two types of subdomains away from the layers. The first subdomain is of O ( log ( 1 / h ) h 1 / 2 ) away from the interior layers and of O ( log ( 1 / h ) h ) away from the boundary layers and the second one is of O ( ? ) away from the outflow of the boundary. Our local error bound for the first subdomain can be improved by a factor of log ( 1 / h ) .  use ighted estimates to prove the first result by constructing new ight functions and the inf-sup condition of the bilinear form to prove the second one."}]