The p‐Version of the Finite Element Method

By Barna Szabó, Alexander Düster, Ernst Rank. 2004

238 citations recorded by the source corpus.

Subfields: Computational Mechanics, Mechanics of Materials, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/370077eaef4b0db245eb3c718b29365ea9d79103

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In Computational Mechanics

In Mechanics of Materials

In Statistics and Probability

Citations in the corpus

An efficient integration technique for the voxel‐based finite cell method (2012, unknown): “Figure 2 provides an overview about the storage requirements of the pre-computed matrices of the present implementation that exploits the hierarchic shape functions of the p-version trunk space [26, 29].”
The p-Version of the Finite Element and Finite Cell Methods (2017, methodology): “The term “p-version of the finite element method” (FEM) first appeared in a publication by Babuška et al. (1981) where the theoretical foundations of a discretization strategy, in which the finite element mesh is fixed and the polynomial degree p of the elements is progressively increased, were…”
Isogeometric analysis : CAD, finite elements, NURBS, exact geometry and mesh refinement (2005, background): “Keywords: NURBS; Finite element analysis; CAD; Structural analysis; Fluid dynamics; Mesh refinement; Convergence; Boundary layers; Internal layers; Geometry; Shells; h-refinement; p-refinement; k-refinement”
Comparison of different higher order finite element schemes for the simulation of Lamb waves (2012, background): “As mentioned before, this property is inherent to isogeometric finite elements and is to be achieved for spectral and p-version finite elements deploying the blending-function method [65, 66, 67, 68, 69, 70, 71].”
Studies of Refinement and Continuity in Isogeometric Structural Analysis (Preprint) (2007, methodology): “[20] for a discussion of the trunk space and the p-method in general).”
Hierarchical theories of structures based on Legendre polynomial expansions with finite element applications (2017, background): “In [33], for example, they underlined the high rates of convergence for properly designed meshes, relying on the possibility of increasing the p-order of the polynomial approximation up to some required level of precision.”
Small and large deformation analysis with the p- and B-spline versions of the Finite Cell Method (2012, methodology): “The high-order basis originally applied in the FCM [28, 29] uses a regular mesh of elements of the p-version of the finite element method, introduced by Szabó and Babuška [30,31,49,50].”
Reduced Bézier element quadrature rules for quadratic and cubic splines in isogeometric analysis (2014, background): “The success of this idea is based on the observation that the higher-order mixed monomials in any tensor-product basis add nothing to the degree of approximation of the solution field [38] (see for example also the construction of trunk spaces in the p-version of the finite element method [74, 75]).”
Comparison of high‐order curved finite elements (2011, methodology): “Thus, in the so-called p-version of FEM (p-FEM, see [4]) the blending function method [5] is usually considered to define an exact mapping relating local and Cartesian coordinates.”
The Finite Cell Method: A Review in the Context of Higher-Order Structural Analysis of CAD and Image-Based Geometric Models (2015, methodology): “Higher-order approximations are used in the p-version of the finite element method [175, 176] and spectral element methods [31,32,71,88].”
The multi-level hp-method for three-dimensional problems: Dynamically changing high-order mesh refinement with arbitrary hanging nodes (2016, background): “in [61, 62], which yields a further increase of the convergence rates as depicted in Figure 10b.”