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Analysis of a stabilized finite element approximation of the transient convection-diffusion-reaction equation using orthogonal subscales. (English) Zbl 0995.65101
The authors analyze a stabilized finite element method to solve the transient convection-diffusion-reaction equation based on the decomposition of the unknowns into resolvable and subgrid scales. They start from the time-discrete form of the problem and obtain an evolution equation for both components of the decomposition. A closed-form expression is proposed for the subscales. An optimal error estimation for the backward Euler methods is given.

MSC:
65M60 Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs
35K57 Reaction-diffusion equations
65M15 Error bounds for initial value and initial-boundary value problems involving PDEs
65M12 Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs
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