Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely:  formulate a sufficient condition on the mesh under which  prove the discrete maximum principle (DMP) for the one-dimensional Poisson equation with Dirichlet boundary conditions discretized by the hp-FEM. The DMP holds if a relative length of every element K in the mesh is bounded by a value H* rel (p) ∈ [0.9,1], where p ≥ 1 is the polynomial degree of the element K. The values H* rel  (p) are calculated for 1 < p < 100.
['Tomáš Vejchodský', 'Pavel Solin']
I am writing a research paper on a idea Discrete Maximum Principle for Higher-Order Finite Elements in 1D
[{"from": "human", "value": "I am writing a research paper on a idea Discrete Maximum Principle for Higher-Order Finite Elements in 1D"}, {"from": "gpt", "value": "Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely:  formulate a sufficient condition on the mesh under which  prove the discrete maximum principle (DMP) for the one-dimensional Poisson equation with Dirichlet boundary conditions discretized by the hp-FEM. The DMP holds if a relative length of every element K in the mesh is bounded by a value H* rel (p) \u2208 [0.9,1], where p \u2265 1 is the polynomial degree of the element K. The values H* rel  (p) are calculated for 1 < p < 100."}]