An error indicator for the calculation of global quantities by the p-adaptive finite element method

Gavrilovic, M.M.; Webb, J.P.

doi:10.1109/20.619685

Cited by 6 publications

(4 citation statements)

References 5 publications

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“…It ooly has ta assess the error relative to the rest of the elements in the mesh. Note aIso that an indicator May be an assessment of the local contribution to a global quantity [65].…”

Section: Global and Localerror Estimatesmentioning

confidence: 99%

“…Many error indicators assess the general quality of the field in an element [74][75][76][77]. It was shown that in problems where a global quantity is desired rather than the field itself, a targeted error indicator (TEl) is a better choice [65]. Sïnce the quantities of interest in the analysis of a microwave deviee are the scattering parameters, a TEl is the most naturaJ choice.…”

Section: Error Indicationmentioning

confidence: 99%

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Accuracy control in the optimization of microwave devices by finite-element methods

Gavrilovic¹,

Webb

2002

IEEE Trans. Microwave Theory Techn.

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“…It ooly has ta assess the error relative to the rest of the elements in the mesh. Note aIso that an indicator May be an assessment of the local contribution to a global quantity [65].…”

Section: Global and Localerror Estimatesmentioning

confidence: 99%

Section: Error Indicationmentioning

confidence: 99%

Accuracy control in the optimization of microwave devices by finite-element methods

Gavrilovic¹,

Webb

2002

IEEE Trans. Microwave Theory Techn.

Self Cite

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“…Generally speaking, three classes of adaptive approaches are available in the literature, including local mesh refinement (h-adaptive), [1][2][3][4][5] moving mesh approach (r-adaptive), 6,7 and a numerical method by locally increasing the degree polynomial of basis functions on selected elements (p-adaptive). 8 For example, an h-adaptive finite element (FEM) method consists of a loop of three key phases: solution, error estimation, and local mesh refinement. The adaptive process is terminated when the acceptable numerical solution is obtained through a posteriori error estimation.…”

Section: Introductionmentioning

confidence: 99%

“…The class of adaptive numerical methods is a practical technique often in conjunction with classical numerical schemes, such as finite elements and finite volumes, to reduce the overall computational cost while obtaining a highly accurate numerical solution. Generally speaking, three classes of adaptive approaches are available in the literature, including local mesh refinement (

h

‐adaptive), 1‐5 moving mesh approach (

r

‐adaptive), 6,7 and a numerical method by locally increasing the degree polynomial of basis functions on selected elements (

p

‐adaptive) 8 . For example, an

h

‐adaptive finite element (FEM) method consists of a loop of three key phases: solution, error estimation, and local mesh refinement.…”

Section: Introductionmentioning

confidence: 99%

Locally adaptive bubble function enrichment for multiscale finite element methods: Application to convection‐diffusion problems

Hwang

2023

Numerical Methods in Fluids

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SummaryWe develop a new class of the multiscale finite element method (MsFEM) to solve the convection‐diffusion problems. In the proposed framework, we decompose the solution function space into two parts in MsFEM with locally adaptive bubble function enrichment (LABFE). The first part is the one that the multiscale basis functions can resolve, and the second part is an unresolved part that is taken care of by a set of bubble functions. These bubble functions are defined similarly to construct multiscale basis functions. We exchange the local‐global information through updated local boundary conditions for these bubble functions. The new multiscale solution recovered from the solution of global numerical formulation provides feedback for updating the local boundary conditions on each coarse element. As the approach iterates, the quality of MsFEM‐LABFE solutions improves since these multiscale basis functions with bubble function enrichment are expected to capture the multiscale feature of the approximate solution more accurately. However, the most expansive part of the algorithm is reconstructing the bubble functions on each coarse element. To reduce the overhead of the bubble function reconstruction, we update the local bubble function only when the intermediate multiscale solution is not well resolved within the region corresponding to the sharp local gradient or the discontinuity of the solution. We illustrate the effectiveness of the proposed method through some numerical examples for convection‐diffusion benchmark problems.

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An Error Estimator for Design Sensitivities of Microwave Device Parameters

Gavrilovic

Webb

2002

Electromagnetics

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An error indicator for the calculation of global quantities by the p-adaptive finite element method

Cited by 6 publications

References 5 publications

Accuracy control in the optimization of microwave devices by finite-element methods

Accuracy control in the optimization of microwave devices by finite-element methods

Locally adaptive bubble function enrichment for multiscale finite element methods: Application to convection‐diffusion problems

An Error Estimator for Design Sensitivities of Microwave Device Parameters

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