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We present an optimal a priori error estimates of the elliptic problems with Dirac sources away from the singular point using discontinuous and enriched Galerkin finite element methods. It is widely shown that the finite element solutions for elliptic problems with Dirac source terms converge sub-optimally in classical norms on uniform meshes. However, here we employ inductive estimates and norm to obtain the optimal order by excluding the small ball regions with the singularities for both two and three dimensional domains. Numerical examples are presented to substantiate our theoretical results.more » « less
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