A fully discrete plates complex on polygonal meshes with application to the Kirchhoff–Love problem
Daniele A. Di Pietro, Jérôme Droniou
Abstract
In this work we develop a novel fully discrete version of the plates complex, an exact Hilbert complex relevant for the mixed formulation of fourth-order problems. The derivation of the discrete complex follows the discrete de Rham paradigm, leading to an arbitrary-order construction that applies to meshes composed of general polygonal elements. The discrete plates complex is then used to derive a novel numerical scheme for Kirchhoff–Love plates, for which a full stability and convergence analysis are performed. Extensive numerical tests complete the exposition.
Topics & Concepts
Polygon meshMathematicsConvergence (economics)Stability (learning theory)Numerical analysisExposition (narrative)Applied mathematicsMathematical analysisCalculus (dental)GeometryComputer scienceEconomic growthMachine learningMedicineEconomicsDentistryArtLiteratureAdvanced Numerical Methods in Computational MathematicsElectromagnetic Simulation and Numerical MethodsNumerical methods in engineering