A high order hybrid mimetic discretization on curvilinear quadrilateral meshes for complex geometries
Yi Zhang (TU Delft - Aerodynamics)
Varun Jain (TU Delft - Aerodynamics)
A Palha da Silva Clerigo (Eindhoven University of Technology, TU Delft - Aerodynamics)
M.I. Gerritsma (TU Delft - Aerodynamics)
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Abstract
In this paper, we present a hybrid mimetic method which solves the mixed formulation of the Poisson problem on curvilinear quadrilateral meshes. The method is hybrid in the sense that the domain is decomposed into multiple disjoint elements and the interelement continuity is enforced using a Lagrange multiplier. The method is mimetic in the sense that the discrete divergence operator is exact. By using the mimetic basis functions and their dual representations, various metric-free discrete terms are obtained. The discrete system can be efficiently solved by first solving a reduced system for the Lagrange multiplier. Numerical experiments which validate the method are presented.