Higher-Order Finite Element Methods

By I. Doležel, K. Segeth, P. Solín. 2003

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MFEM: a modular finite element methods library (2019, methodology): “ions. The FormLinearSystem method also supports two more advanced and closely related techniques for reducing the size of a nite element linear system: hybridization and static condensation, see e.g. [84, 17]. Note that hybridization in MFEM is applied to a single bilinear form, see [39], instead of”
The generation of arbitrary order curved meshes for 3D finite element analysis (2013, background): “The last decade has seen an increase in interest in the development of high-order discretisation methods within the finite element community [29,15,11,16].”
A SET OF SYMMETRIC QUADRATURE RULES ON TRIANGLES AND TETRAHEDRA (2009, methodology): “Many methods have been developed for computing quadrature rules; we refer the reader to [1, 2, 3, 4, 5, 6, 7, 8, 9] and the references therein.”
Comparison of different higher order finite element schemes for the simulation of Lamb waves (2012, methodology): “Following the approach first established by Szabó and Babuška [33] and seized by many others [46,47,32,48,49] it is shown how hierarchic basis functions can be generated up to any desired polynomial degree.”
Simulation Methods for Guided Wave-Based Structural Health Monitoring: A Review (2015, methodology): “Since adaptive refinement is beyond the scope of this treatise the reader is referred to [50, 51, 237].”