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math.NA2022
A generalized framework for direct discontinuous Galerkin methods for nonlinear diffusion equations
Mustafa Engin Danis, Jue Yan
In this study, we propose a unified, general framework for the direct discontinuous Galerkin methods. In the new framework, the antiderivative of the nonlinear diffusion matrix is…
math.NA2022
Cell-average based neural network method for high dimensional parabolic differential equations
Hong Zhang, Hongying Huang, Jue Yan
In this paper, we introduce cell-average based neural network (CANN) method to solve high-dimensional parabolic partial differential equations. The method is based on the integral…