Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely:  introduces a numerical scheme for the time-harmonic Maxll equations by using ak Galerkin (WG) finite element methods. The WG finite element method is based on two operators: discrete ak curl and discrete ak gradient, with appropriately defined stabilizations that enforce a ak continuity of the approximating functions. This WG method is highly flexible by allowing the use of discontinuous approximating functions on arbitrary shape of polyhedra and, at the same time, is parameter free. Optimal-order of convergence is established for the WG approximations in various discrete norms which are either $$H^1$$H1-like or $$L^2$$L2 and $$L^2$$L2-like. An effective implementation of the WG method is developed through variable reduction by following a Schur-complement approach, yielding a system of linear equations involving unknowns associated with element boundaries only. Numerical results are presented to confirm the theory of convergence.
['Lin Mu', 'Junping Wang', 'Xiu Ye', 'Shangyou Zhang']
I am writing a research paper on a idea A Weak Galerkin Finite Element Method for the Maxwell Equations
[{"from": "human", "value": "I am writing a research paper on a idea A Weak Galerkin Finite Element Method for the Maxwell Equations"}, {"from": "gpt", "value": "Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely:  introduces a numerical scheme for the time-harmonic Maxll equations by using ak Galerkin (WG) finite element methods. The WG finite element method is based on two operators: discrete ak curl and discrete ak gradient, with appropriately defined stabilizations that enforce a ak continuity of the approximating functions. This WG method is highly flexible by allowing the use of discontinuous approximating functions on arbitrary shape of polyhedra and, at the same time, is parameter free. Optimal-order of convergence is established for the WG approximations in various discrete norms which are either $$H^1$$H1-like or $$L^2$$L2 and $$L^2$$L2-like. An effective implementation of the WG method is developed through variable reduction by following a Schur-complement approach, yielding a system of linear equations involving unknowns associated with element boundaries only. Numerical results are presented to confirm the theory of convergence."}]