Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely: In this work  present an a posteriori output error bound for model order reduction of parametrized evolution equations. With the help of the dual system and a simple representation of the relationship beten the field variable error and the residual of the primal system, a sharp output error bound is derived. Such an error bound successfully avoids the accumulation of the residual over time, which is a common drawback in the existing error estimations for time-stepping schemes. An estimation needs to be performed for practical computation of the error bound, and as a result, the output error bound reduces to an output error estimation. The proposed error estimation is applied to four kinds of problems. The first one is a linear convection-diffusion equation, which is used to compare the performance of the new error estimation and an existing primal-dual error bound. The second one is the unsteady viscous Burgers' equation, an academic benchmark of nonlinear evolution equations in fluid dynamics often u...
['Yongjin Zhang', 'Lihong Feng', 'Suzhou Li', 'Peter Benner']
I am writing a research paper on a idea An Efficient Output Error Estimation for Model Order Reduction of Parametrized Evolution Equations
[{"from": "human", "value": "I am writing a research paper on a idea An Efficient Output Error Estimation for Model Order Reduction of Parametrized Evolution Equations"}, {"from": "gpt", "value": "Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely: In this work  present an a posteriori output error bound for model order reduction of parametrized evolution equations. With the help of the dual system and a simple representation of the relationship beten the field variable error and the residual of the primal system, a sharp output error bound is derived. Such an error bound successfully avoids the accumulation of the residual over time, which is a common drawback in the existing error estimations for time-stepping schemes. An estimation needs to be performed for practical computation of the error bound, and as a result, the output error bound reduces to an output error estimation. The proposed error estimation is applied to four kinds of problems. The first one is a linear convection-diffusion equation, which is used to compare the performance of the new error estimation and an existing primal-dual error bound. The second one is the unsteady viscous Burgers' equation, an academic benchmark of nonlinear evolution equations in fluid dynamics often u..."}]