Lower a posteriori error estimates on anisotropic meshes

Kopteva, Natalia

doi:10.1007/s00211-020-01137-9

Cited by 4 publications

(3 citation statements)

References 12 publications

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“…The linear elements in our groundwater model do account for sediment anisotropy. However, due to the skewness of the elements, errors may be introduced (e.g., Balan et al., 2022; Huang et al., 2017; Kopteva, 2020a, 2020b). Additional numerical simulations we carried out (Figures S5–S7 in Supporting Information S1) suggest that there is no evidence of numerical errors based on grid refinement.…”

Section: Discussionmentioning

confidence: 99%

“…For this reason, the onshore component of the groundwater systems was not considered, and we were unable to take into account the variability of climatic parameters (e.g., precipitation, temperature, land use, and ice cover). The linear elements in our groundwater model do account for sediment anisotropy. However, due to the skewness of the elements, errors may be introduced (e.g., Balan et al., 2022; Huang et al., 2017; Kopteva, 2020a, 2020b). Additional numerical simulations we carried out (Figures S5–S7 in Supporting Information S1) suggest that there is no evidence of numerical errors based on grid refinement. The generated stratigraphic models are simplified and do not include the fine‐scale heterogeneity observed in field data.…”

Section: Discussionmentioning

confidence: 99%

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Can Offshore Meteoric Groundwater Generate Mechanical Instabilities in Passive Continental Margins?

et al. 2023

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Offshore meteoric groundwater (OMG) has long been hypothesized to be a driver of seafloor geomorphic processes in continental margins worldwide. Testing this hypothesis has been challenging because of our limited understanding of the distribution and rate of OMG flow and seepage, and their efficacy as erosive/destabilizing agents. Here we carry out numerical simulations of groundwater flow and slope stability using conceptual models and evolving stratigraphy—for passive siliciclastic and carbonate margin cases—to assess whether OMG and its evolution during a late Quaternary glacial cycle can generate the pore pressures required to trigger mechanical instabilities on the seafloor. Conceptual model results show that mechanical instabilities using OMG flow are most likely to occur in the outer shelf to upper slope, at or shortly before the Last Glacial Maximum sea‐level lowstand. Models with evolving stratigraphy show that OMG flow is a key driver of pore pressure development and instability in the carbonate margin case. In the siliciclastic margin case, OMG flow plays a secondary role in preconditioning the slope to failure. The higher degree of spatial/stratigraphic heterogeneity of carbonate margins, lower shear strengths of their sediments, and limited generation of overpressures by sediment loading may explain the higher susceptibility of carbonate margins, in comparison to siliciclastic margins, to mechanical instability by OMG flow. OMG likely played a more significant role in carbonate margin geomorphology (e.g., Bahamas, Maldives) than currently thought.

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Section: Discussionmentioning

confidence: 99%

Section: Discussionmentioning

confidence: 99%

Can Offshore Meteoric Groundwater Generate Mechanical Instabilities in Passive Continental Margins?

et al. 2023

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“…Then, the bubble functions b F will be independent of the individual face size and the number of elements. For instance, this is the approach used in [31] to derive a lower bound of the flux residual of the FEM employing structured anisotropic triangular meshes. However, the construction of such face bubble functions for the general-shaped polytopic meshes considered in this work is highly non-trivial.…”

Section: Flux Residualsmentioning

confidence: 99%

A posteriori error estimates for discontinuous Galerkin methods on polygonal and polyhedral meshes

Cangiani¹,

Dong²,

Georgoulis³

2022

Preprint

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We present a new residual-type energy-norm a posteriori error analysis for interior penalty discontinuous Galerkin (dG) methods for linear elliptic problems. The new error bounds are also applicable to dG methods on meshes consisting of elements with very general polygonal/polyhedral shapes. The case of simplicial and/or box-type elements is included in the analysis as a special case. In particular, for the upper bounds, arbitrary number of very small faces are allowed on each polygonal/polyhedral element, as long as certain mild shape regularity assumptions are satisfied. As a corollary, the present analysis generalizes known a posteriori error bounds for dG methods, allowing in particular for meshes with arbitrary number of irregular hanging nodes per element. The proof hinges on a new conforming recovery strategy in conjunction with a Helmholtz decomposition formula. The resulting a posteriori error bound involves jumps on the tangential derivatives along elemental faces. Local lower bounds are also proven for a number of practical cases. Numerical experiments is also presented, highlighting the practical value of the derived a posteriori error bounds as error estimators.

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