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We propose a weak Galerkin (WG) finite element method for solving one-dimensional nonlinear convection–diffusion problems. Based on a weak form, the semi-discrete WG finite element scheme is established and analyzed. We prove the stability of the semi-discrete solution and derive the optimal order error estimate in the discrete $$H^1$$ H1 -norm and $$L^2$$ L2 -norm, respectively. Numerical experiment...
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