Three direct discontinuous Galerkin methods on a Bakhvalov‐type mesh for a singularly perturbed reaction‐diffusion problem

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The direct discontinuous Galerkin (DDG) methods on a Bakhvalov‐type mesh are developed to solve a singularly perturbed reaction‐diffusion problem. First, we introduce and analyze a unified, generalized framework for the DDG methods. Then, the parameter‐uniform convergence rate of our numerical method in the balanced norm is established by using the local weighted ‐projection, where represents the degree of the piecewise polynomial space. Finally, some numerical results are presented to further validate our theoretical findings.