Design and analysis of the Extended Hybrid High-Order method for the Poisson problem

Liam, Yemm,

doi:10.1007/s10444-022-09958-y

Cited by 5 publications

(3 citation statements)

References 43 publications

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“…Although the machine learning method is effective, its model does not have a clear reflection in the interpretation of prediction results. On the one hand, such as deep neural networks or complex models, this type of method usually has high accuracy, but the internal principles and mechanisms of these methods and models are difficult to understand, and the influence of features on the model prediction results cannot be obtained [9][10][11]. On the other hand, simple models like linear regression and decision trees usually have better interpretability, but their predictive power is usually limited and their accuracy is lower.…”

Section: Introductionmentioning

confidence: 99%

Problem Analysis and Application Research in Legal Judgment Prediction Based on Data Mining

2024

jes

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The judgments of some hot cases that exceeded public expectations seem to confirm this. Although the legal certainty is questioned, the judgment remains predictable. The predictability of judgments is a way to enhance judicial authority and maintain judicial credibility. It is also a way to achieve overlapping consensus between the judiciary and the public, provide stable value guidance and behavioral expectations for the public, and promote the generation and development of public rational trust. To enhance public legal trust by improving the predictability of judgments, it is necessary to increase the burden of reasoning for judicial judgments, avoid randomness and contingency, and ensure the adequate provision and substantial disclosure of previous judgment information, so that judgment prediction in the era of big data can truly become possible. The research is to use the optimized particle swarm algorithm as the underlying model to carry out joint modeling and prediction research on the analysis and application of problems in the prediction of legal judgments. According to experimental calculations, the optimized particle swarm algorithm can significantly improve the accuracy and universality of legal judgment prediction. After optimization, the convergence speed is increased by about 5%, and the value of the acceleration factor is more significant.

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Section: Introductionmentioning

confidence: 99%

Problem Analysis and Application Research in Legal Judgment Prediction Based on Data Mining

2024

jes

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“…However, this method does not capture the geometry exactly and requires a finely tuned Nitsche parameter to achieve stability and consistency [cf.30]. Moreover, without unknowns defined on curved faces, it is not clear how to design an enriched method such as that proposed in [38], whereas the method devised in this paper works seamlessly with enrichment.…”

Section: Introductionmentioning

confidence: 99%

“…In this paper, we take inspiration from the article [38] and consider unknowns on the faces to include the Neumann traces of higher-order polynomials. We note that this approach does not consider reference elements or faces but rather directly defines non-polynomial spaces on curved faces.…”

Section: Introductionmentioning

confidence: 99%

A New Approach to Handle Curved Meshes in the Hybrid High-Order Method

Liam

2023

Found Comput Math

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We present here a novel approach to handling curved meshes in polytopal methods within the framework of hybrid high-order methods. The hybrid high-order method is a modern numerical scheme for the approximation of elliptic PDEs. An extension to curved meshes allows for the strong enforcement of boundary conditions on curved domains and for the capture of curved geometries that appear internally in the domain e.g. discontinuities in a diffusion coefficient. The method makes use of non-polynomial functions on the curved faces and does not require any mappings between reference elements/faces. Such an approach does not require the faces to be polynomial and has a strict upper bound on the number of degrees of freedom on a curved face for a given polynomial degree. Moreover, this approach of enriching the space of unknowns on the curved faces with non-polynomial functions should extend naturally to other polytopal methods. We show the method to be stable and consistent on curved meshes and derive optimal error estimates in $$L^2$$ L 2 and energy norms. We present numerical examples of the method on a domain with curved boundary and for a diffusion problem such that the diffusion tensor is discontinuous along a curved arc.

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Enriched virtual elements for plane elasticity with corner singularities

Artioli,

Mascotto

2023

Comput Mech

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Design and analysis of the Extended Hybrid High-Order method for the Poisson problem

Cited by 5 publications

References 43 publications

Problem Analysis and Application Research in Legal Judgment Prediction Based on Data Mining

Problem Analysis and Application Research in Legal Judgment Prediction Based on Data Mining

A New Approach to Handle Curved Meshes in the Hybrid High-Order Method

Enriched virtual elements for plane elasticity with corner singularities

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