Collaborative Proposal: SGER: Conforming Polygonal Finite Elements

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In this Small Grant Exploratory Research proposal, a new and novel direction in finite element methodology is pursued. Polygonal finite elements provide greater flexibility in mesh generation and are better-suited for applications in solid mechanics which involve a significant change in the topology of the material domain. In this proposal, recent advances in meshfree approximations, computational geometry, and computer graphics will be used to construct conforming trial and test approximations onpolygonal finite elements. Computational algorithms (optimization scheme) for mesh generation with polygonal elements will be developed, and numerical studies on the accuracy and convergenceof the finite element technique will be conducted forelliptic boundary-value problems. The results of this study can potentially open-up new pathways in finite element research, lead to the wider usage of polygonal finite element methods in solid mechanicsand computational materials science, and also provide impetus for the construction of cubature rules on polytopes.