%0 Journal Article %1 droniou2016gradient %A Droniou, Jérome %A Eymard, Robert %A Herbin, Raphaèle %D 2016 %I EDP Sciences %J ESAIM: Mathematical Modelling and Numerical Analysis %K 35k05-heat-equation 65m08-pdes-ibvps-finite-volumes 65m12-pdes-ivps-stability-and-convergence-of-numerical-methods 65m60-pdes-ibvps-finite-elements %N 3 %P 749--781 %R 10.1051/m2an/2015079 %T Gradient schemes: Generic tools for the numerical analysis of diffusion equations %U https://doi.org/10.1051%2Fm2an%2F2015079 %V 50 %X The gradient scheme framework is based on a small number of properties and encompasses a large number of numerical methods for diffusion models. We recall these properties and develop some new generic tools associated with the gradient scheme framework. These tools enable us to prove that classical schemes are indeed gradient schemes, and allow us to perform a complete and generic study of the well-known (but rarely well-studied) mass lumping process. They also allow an easy check of the mathematical properties of new schemes, by developing a generic process for eliminating unknowns via barycentric condensation, and by designing a concept of discrete functional analysis toolbox for schemes based on polytopal meshes.

@article{droniou2016gradient, abstract = {The gradient scheme framework is based on a small number of properties and encompasses a large number of numerical methods for diffusion models. We recall these properties and develop some new generic tools associated with the gradient scheme framework. These tools enable us to prove that classical schemes are indeed gradient schemes, and allow us to perform a complete and generic study of the well-known (but rarely well-studied) mass lumping process. They also allow an easy check of the mathematical properties of new schemes, by developing a generic process for eliminating unknowns via barycentric condensation, and by designing a concept of discrete functional analysis toolbox for schemes based on polytopal meshes.}, added-at = {2021-03-14T23:41:49.000+0100}, author = {Droniou, Jérome and Eymard, Robert and Herbin, Raphaèle}, biburl = {https://www.bibsonomy.org/bibtex/2ebc729068fb8b70429c883f30a1b0c4d/gdmcbain}, doi = {10.1051/m2an/2015079}, interhash = {d9ad66a39d9b92d6486f348167db5bf7}, intrahash = {ebc729068fb8b70429c883f30a1b0c4d}, journal = {{ESAIM}: Mathematical Modelling and Numerical Analysis}, keywords = {35k05-heat-equation 65m08-pdes-ibvps-finite-volumes 65m12-pdes-ivps-stability-and-convergence-of-numerical-methods 65m60-pdes-ibvps-finite-elements}, month = may, number = 3, pages = {749--781}, publisher = {{EDP} Sciences}, timestamp = {2021-03-14T23:41:49.000+0100}, title = {Gradient schemes: Generic tools for the numerical analysis of diffusion equations}, url = {https://doi.org/10.1051%2Fm2an%2F2015079}, volume = 50, year = 2016 }