Toward a universal adaptive finite element strategy, part 1. Constrained approximation and data structure

Demkowicz, Leszek; Oden, J. T.; Rachowicz, Waldemar; Hardy, O.

doi:10.1016/0045-7825(89)90129-1

Cited by 392 publications

(176 citation statements)

References 7 publications

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“…where the quantity in brackets is the interpolated gradient, q5i,i+5,j, at m. This reduces to (15) when a = 1, and provides a second-order accurate approximation of the fluxes through cell edges.…”

Section: Two-dimensional Casementioning

confidence: 99%

A Cartesian Grid Embedded Boundary Method for Poisson's Equation on Irregular Domains

Johansen

Colella

1998

Journal of Computational Physics

413

406

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We present a numerical method for solving Poisson's equation, with variable coefficients and Dirichlet boundary conditions, on two-dimensional regions. The approach uses a fhite-volume discretization, which embeds the domain in a regular Cartesian grid. We treat the solution as a cell-centered quantity, even when those centers are outside the domain. Cells that contain a portion of the domain boundafy use conservative differencing of second-order accurate fluxes, on each cell volume. The calculation of the boundary flux ensures that the conditioning of the matrix is relatively unaffected by small cell volumes. This allows us to use multi-grid iterations with a simple point relaxation strategy. We have, combined this with an adaptive mesh refinement (AMR) procedure. We provide evidence that the algorithm is second-order accurate on various exact solutions, and compare the adaptive and non-adaptive calculations.

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Section: Two-dimensional Casementioning

confidence: 99%

A Cartesian Grid Embedded Boundary Method for Poisson's Equation on Irregular Domains

Johansen

Colella

1998

Journal of Computational Physics

413

406

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“…In addition, to maintain continuity of global basis function, constraints at the interface of elements supporting edge functions of different order are employed. The constraint represents a generalization of the hp-constraints, which is discussed in Demkowicz et al [10].…”

Section: Hp Constraints Are Employed To Meet Continuity Requirementsmentioning

confidence: 99%

Comparison of h-, p- and hp-adaptation for convective heat transfer

Pepper¹,

Wang²

2007

WIT Transactions on Modelling and Simulation, Vol 46

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Three adaptive FEM algorithms based on mesh refinement (h-adaptation), mesh enrichment (p-adaptation) and the combination of both (hp-adaptation) are employed to solve incompressible fluid flow problems including convective heat transfer effects. Test cases of natural convection in a square cavity with different Rayleigh numbers are solved using primitive variables in a modified finite element approach employing the three adaptive strategies. Results show excellent agreement among benchmark data available in the literature.

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“…A general approach to hp-adaptive methods was developed in a series of papers by Oden, Demkowicz, Rachowicz, and others, see [41][42][43]. There a general data structure, constructed on quadrilateral or hexahedral meshes, was developed which provided for irregular h refinements and p enrichments.…”

Section: Number Of Gridmentioning

confidence: 99%

Modeling and Computational Analysis of Multiscale Phenomena in Fluid-Structure Interaction Problems

Oden¹

1992

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Toward a universal adaptive finite element strategy, part 1. Constrained approximation and data structure

Cited by 392 publications

References 7 publications

A Cartesian Grid Embedded Boundary Method for Poisson's Equation on Irregular Domains

A Cartesian Grid Embedded Boundary Method for Poisson's Equation on Irregular Domains

Comparison of h-, p- and hp-adaptation for convective heat transfer

Modeling and Computational Analysis of Multiscale Phenomena in Fluid-Structure Interaction Problems

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