Abstract
Previously, we developed Eulerian–Lagrangian localized adjoint methods (ELLAMs) to solve advection-reaction problems. ELLAMs provide a systematic approach to treat boundary conditions and to conserve mass and have proven to be powerful methods for advection-dominated problems. In this paper, the authors conduct theoretical analysis for these ELLAMs and prove that they have an optimal-order convergence rate. Moreover, the estimates involve only the derivatives of the exact solution in space and along the characteristics. In contrast, many existing methods have only suboptimal-order error estimates for advection-reaction problems and the estimates involve the temporal derivatives of the exact solution, which are usually much larger than the derivatives along the characteristics.Key words. advection-reaction equations, Eulerian–Lagrangian method, convergence analysis, optimal-order error estimates
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