Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely:  consider an interior penalty discontinuous approximation for symmetric elliptic problems of second order on non-matching grids in this paper. The main result is an almost optimal error estimate for the interior penalty approximation of the original problem based on partitioning of the domain into a finite number of subdomains. Further, an error analysis for the finite element approximation of the penalty formulation is given. Finally, numerical experiments on a series of model second order problems are presented.
['Raytcho D. Lazarov', 'Joseph E. Pasciak', 'Joachim Schöberl', 'Panayot S. Vassilevski']
I am writing a research paper on a idea Almost optimal interior penalty discontinuous approximations of symmetric elliptic problems on non-matching grids
[{"from": "human", "value": "I am writing a research paper on a idea Almost optimal interior penalty discontinuous approximations of symmetric elliptic problems on non-matching grids"}, {"from": "gpt", "value": "Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely:  consider an interior penalty discontinuous approximation for symmetric elliptic problems of second order on non-matching grids in this paper. The main result is an almost optimal error estimate for the interior penalty approximation of the original problem based on partitioning of the domain into a finite number of subdomains. Further, an error analysis for the finite element approximation of the penalty formulation is given. Finally, numerical experiments on a series of model second order problems are presented."}]