Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely: Most results related to discrete nonnegativity conservation principles (DNCP) for elliptic problems are limited to finite differences and lost-order finite element methods (FEM).   show that a straightforward extension to higher-order finite element methods (hp-FEM) in the classical sense is not possible.  formulate a aker DNCP for the Poisson equation in one spatial dimension and prove it using an interval computing technique. Numerical experiments related to the extension of this result to 2D are presented.
['Pavel Solin', 'Tomáš Vejchodský', 'Roberto Araiza']
I am writing a research paper on a idea Discrete conservation of nonnegativity for elliptic problems solved by the hp-FEM
[{"from": "human", "value": "I am writing a research paper on a idea Discrete conservation of nonnegativity for elliptic problems solved by the hp-FEM"}, {"from": "gpt", "value": "Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely: Most results related to discrete nonnegativity conservation principles (DNCP) for elliptic problems are limited to finite differences and lost-order finite element methods (FEM).   show that a straightforward extension to higher-order finite element methods (hp-FEM) in the classical sense is not possible.  formulate a aker DNCP for the Poisson equation in one spatial dimension and prove it using an interval computing technique. Numerical experiments related to the extension of this result to 2D are presented."}]