Hermite analogs of the lowest order Raviart–Thomas mixed method for convection–diffusion equations

Abstract : The Raviart-Thomas mixed finite element method of the lowest order [19] commonly known as the RT 0 method, is a well-established and popular numerical tool to solve diffusion-like problems providing flux continuity across inter-element boundaries. Douglas & Roberts extended the method to the case of more general second order boundary value problems including the convection-diffusion equations (cf. this journal [10]). The main drawback of these methods however is the poor representation of the primal variable by piecewise constant functions. The Hermite analog of the RT 0 method for treating pure diffusion phenomena proposed in [21] proved to be a valid alternative to attain higher order approximation of the primal variable, while keeping intact the matrix structure and the quality of the discrete flux variable of the original RT 0 method. Non trivial extensions of this method are studied here, that can be viewed as Hermite analogs of the two Douglas & Roberts' versions of the RT 0 method, to solve convection-diffusion equations. A detailed convergence study is carried out for one of the Hermite methods, and numerical results illustrate the performance of both of them, as compared to each other and to the corresponding mixed methods.
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Computational and Applied Mathematics, Springer Verlag, 2017, pp.1-21. 〈10.1007/s40314-017-0474-5〉
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V. Ruas, F. A. Radu. Hermite analogs of the lowest order Raviart–Thomas mixed method for convection–diffusion equations. Computational and Applied Mathematics, Springer Verlag, 2017, pp.1-21. 〈10.1007/s40314-017-0474-5〉. 〈hal-01590830〉

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