Higher-order finite element methods

By Raytcho D. Lazarov. Mathematics of Computation, 2005

352 citations recorded by the source corpus.

View Paper: https://www.semanticscholar.org/paper/2267f78b76634eef6cb4aeec962a81e388f2c6d9

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

Citations in the corpus

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.”
A new second-order numerical manifold method model with an efficient scheme for analyzing free surface flow with inner drains (2016, methodology): “Based on finite covers, the NMM is flexible and general enough to include and combine well-developed analytical methods, the widely-used FEM, and the block-oriented discontinuous deformation analysis (DDA, [44]) in a unified form.”
The generation of arbitrary order curved meshes for 3D finite element analysis (2013, methodology): “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].”
Use of higher‐order shape functions in the scaled boundary finite element method (2006, methodology): “Equations (31) and (33) together define the Lobatto polynomials, a hierarchical set of polynomial functions leading to well-conditioned element stiffness matrices, ideal for use in higher-order finite element methods [11, 13].”
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].”
The hp‐d‐adaptive finite cell method for geometrically nonlinear problems of solid mechanics (2012, methodology): “For a detailed discussion of its mathematical characteristics and hprefinement strategies for its efficient numerical solution, see [27,28,83,84].”
A unified approach for a posteriori high-order curved mesh generation using solid mechanics (2016, methodology): “The performance of high-order discretisation methods for the simulation of various problems in science and engineering has been the object of intensive research during the last twodecades [32,41,44,67].”
p-Multigrid solution of high-order discontinuous Galerkin discretizations of the compressible Navier-Stokes equations (2005, methodology): “In this work, two types of basis functions are used: a nodal Lagrange basis with equispaced nodes, and a hierarchical basis composed of vertex, edge, and bubble functions, as described in [19].”
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.”
Automated Solution of Differential Equations by the Finite Element Method: The FEniCS Book (2012, background): “Quadrature rules for a variety of reference elements may be obtained from for example (Dunavant, 1985; Keegan et al., 2008; Šolín et al., 2004).”