An arbitrary-order discrete rot-rot complex on polygonal meshes with application to a quad-rot problem

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چکیده

Abstract In this work, following the discrete de Rham approach, we develop a counterpart of two-dimensional complex with enhanced regularity. The proposed construction supports general polygonal meshes and arbitrary approximation orders. We establish exactness on contractible domain for both versions without boundary conditions and, former, prove complete set Poincaré-type inequalities. is then used to derive novel discretization method quad-rot problem, which, unlike other schemes in literature, does not require forcing term be prepared. carry out stability convergence analyses scheme provide numerical validation results.

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ژورنال

عنوان ژورنال: Ima Journal of Numerical Analysis

سال: 2023

ISSN: ['1464-3642', '0272-4979']

DOI: https://doi.org/10.1093/imanum/drad045