A priori mesh quality metric error analysis applied to a high-order finite element method

Lowrie, Weston; Lukin, V. S.; Shumlak, U.

doi:10.1016/j.jcp.2011.03.036

Cited by 20 publications

(14 citation statements)

References 14 publications

(34 reference statements)

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“…This work was evaluated in [25], and presented favorable agreement between numerical error and the mesh quality indicators derived in [8]. This was a motivation for the extension to three-dimensions [7], and further to focus the work on the quality assessment of interfaces of three-dimensional hybrid grids, as well as on its improvement.…”

Section: Introductionmentioning

confidence: 85%

Quality Index and Improvement of the Interfaces of General Hybrid Grids

Fotia

Kallinderis

2014

Procedia Engineering

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Hybrid grids constitute a significant class of meshes for complex-geometry flow simulations. They consist of prisms and/or hexahedra covering viscous regions primarily, while tetrahedra discretize the rest of the domain with pyramids serving as transitional elements. The local changes in element topology form grid interfaces. This is especially so for cases where the number of prisms/hexahedra per layer (stack) is not constant ("chopped" layers). The present work deals with the quality of the interfaces encountered in general hybrid grids with non-constant number of layers. A priori estimation of the quality is based on truncation error terms. Four representative types of interfaces are considered. The effect of grid stretching and skewness was examined for the interfaces. Further, the quality is improved via repositioning of the central point of each of the interface types. The improvement is quantified via application to several hybrid grids.

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Section: Introductionmentioning

confidence: 85%

Quality Index and Improvement of the Interfaces of General Hybrid Grids

Fotia

Kallinderis

2014

Procedia Engineering

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“…Examples of this work include Lu et al [7,8] and Lowrie et al [9]. In [7], the quality of a curved high-order element is considered to be the product of the following two quantities: (a) the quality of a straight-sided linear element with the identical location of the corner vertices, and (b), the ratio of the largest and the smallest value of the determinant of the Jacobian matrix of the physical coordinate system with respect to the parametric coordinate system.…”

Section: Related Workmentioning

confidence: 99%

“…In [7], the quality of a curved high-order element is considered to be the product of the following two quantities: (a) the quality of a straight-sided linear element with the identical location of the corner vertices, and (b), the ratio of the largest and the smallest value of the determinant of the Jacobian matrix of the physical coordinate system with respect to the parametric coordinate system. Lowrie et al's [9] paper looks at the correlation between the quality metric for a linear element and the solution accuracy for high-order meshes through a series of numerical experiments.…”

Section: Related Workmentioning

confidence: 99%

On Interpolation Errors over Quadratic Nodal Triangular Finite Elements

Sastry

Kirby

2014

Proceedings of the 22nd International Meshing Roundtable

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Summary. Interpolation techniques are used to estimate function values and their derivatives at those points for which a numerical solution of any equation is not explicitly evaluated. In particular, the shape functions are used to interpolate a solution (within an element) of a partial differential equation obtained by the finite element method. Mesh generation and quality improvement are often driven by the objective of minimizing the bounds on the error of the interpolated solution. For linear elements, the error bounds at a point have been derived as a composite function of the shape function values at the point and its distance from the element's nodes. We extend the derivation to quadratic triangular elements and visualize the bounds for both the function interpolant and the interpolant of its derivative. The maximum error bound for a function interpolant within an element is computed using the active set method for constrained optimization. For the interpolant of the derivative, we visually observe that the evaluation of the bound at the corner vertices is sufficient to find the maximum bound within an element. We characterize the bounds and develop a mesh quality improvement algorithm that optimizes the bounds through the movement (r-refinement) of both the corner vertices and edge nodes in a high-order mesh.

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“…Analytic expressions that relate the TE with the distortions have been derived for linear grids . Comparisons of commonly used a priori mesh quality metrics have also been reported . The field‐related terms of the TE expressions are typically used as indicators for solution‐based grid adaptation , , …”

Section: Introductionmentioning

confidence: 99%

A study of properties of adaptive quadratic grids for three‐dimensional near‐surface field computations

Kallinderis

Lymperopoulou

Spyridonos

et al. 2019

Numerical Methods in Fluids

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Summary Curved geometries and the corresponding near‐surface fields typically require a large number of linear computational elements. High‐order numerical solvers have been primarily used with low‐order meshes. There is a need for curved, high‐order computational elements. Typical near‐surface meshes consist of hexahedral and/or prismatic elements. The present work studies the employment of quadratic meshes that are relatively coarse for field simulations. Directionally quadratic high‐order elements are proposed for the near‐surface field regions. The quadratic meshes are compared with the conventional low‐order ones in terms of accuracy and efficiency. The cases considered include closed surface volume calculations, as well as computation of gradients of several analytic fields. A special method of adaptive local quadratic meshes is proposed and evaluated. Truncation error analysis for quadratic grids yields comparison with the conventional linear hexahedral/prismatic meshes, which are subject to typical distortions such as stretching, skewness, and torsion.

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A priori mesh quality metric error analysis applied to a high-order finite element method

Cited by 20 publications

References 14 publications

Quality Index and Improvement of the Interfaces of General Hybrid Grids

Quality Index and Improvement of the Interfaces of General Hybrid Grids

On Interpolation Errors over Quadratic Nodal Triangular Finite Elements

A study of properties of adaptive quadratic grids for three‐dimensional near‐surface field computations

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