The adaptive finite element method for the P-Laplace problem

Liu, D.J.; Chen, Z.R.

doi:10.1016/j.apnum.2019.11.018

Cited by 6 publications

(8 citation statements)

References 21 publications

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“…Various computable a posteriori error estimates have recently been derived for convex minimization problems such as the p-Dirichlet problem or degenerate minimization problems, cf. [21,12,33,32,9]. These a posteriori error estimates are typically defined for a particular finite element method and an appropriate discretization of the problem including a suitable choice of quadrature.…”

Section: Available Estimatesmentioning

confidence: 99%

“…[8]. The reconstruction formula (1.8) was also referred to in [33,32] in the case of the non-linear Dirichlet problem. However, the different a posteriori error estimates derived therein rely less on convex duality arguments such as, e.g., (1.4) or (1.9) do, but more on the reconstruction of an S 3 D (T h )-conformal 2 companion, which is computationally cheap but rather indirect.…”

Section: New Contributionsmentioning

confidence: 99%

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Explicit and efficient error estimation for convex minimization problems

Bartels¹,

Kaltenbach²

2022

Preprint

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We combine a systematic approach for deriving general a posteriori error estimates for convex minimization problems based on convex duality relations with a recently derived generalized Marini formula. The a posteriori error estimates are essentially constantfree and apply to a large class of variational problems including the p-Dirichlet problem, as well as degenerate minimization, obstacle and image de-noising problems. In addition, these a posteriori error estimates are based on a comparison to a given non-conforming finite element solution. For the p-Dirichlet problem, these a posteriori error bounds are equivalent to residual type a posteriori error bounds and, hence, reliable and efficient.

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Section: Available Estimatesmentioning

confidence: 99%

Section: New Contributionsmentioning

confidence: 99%

Explicit and efficient error estimation for convex minimization problems

Bartels¹,

Kaltenbach²

2022

Preprint

View full text Add to dashboard Cite

show abstract

“…Secondly, calculate the regional energy of the layer where the sum is located, as shown in equation (7).…”

Section: Integration Processmentioning

confidence: 99%

“…Then, minh.n.do proposed quantization and threshold method [5], which made image fusion enter a new stage. Image fusion [6][7] refers to the collection of the same target image information through multi-channel, through information extraction, enhancement, denoising or other computer technology, to collect the effective information in the image, and finally generate the image with the largest amount of information. Under the same target, multiple different source images are fused by operator or neural network to form a new image with multiple information.…”

Section: Introductionmentioning

confidence: 99%

Image Fusion Algorithm in Integrated Space-Ground-Sea Wireless Networks of B5G

Cui

Wang

et al. 2021

Preprint

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In recent years, in Space-Ground-Sea Wireless Networks, the rapid development of image recognition also promotes the development of images fusion. For example, the content of single-mode medical image is very single, and the fused image contains more image information, which provides a more reliable basis for diagnosis. However, in wireless communication and medical image processing, the image fusion effect is poor and the efficiency is low. To solve this problem, a image fusion algorithm based on fast finite shear wave transform and convolutional neural network is proposed for wireless communication. Firstly, the source image is decomposed by fast finite shear wave transform (FFST); secondly, the convolution neural network is improved to reduce the dimension of convolution layer from two steps, and the number of iterations and the optimal weight of convolution neural network are determined by experiments; finally, the image is fused by the inverse process of fast finite shear wave transform. The experimental results show that the algorithm has a very good effect in both objective indicators and subjective vision, and it is also very feasible in wireless communication.

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“…Then, Akhtarkavan et al proposed the quantization and threshold method [5], which made image fusion enter a new stage. Image fusion [6,7] refers to the collection of the same target image information through multi-channel, through information extraction, enhancement, denoising, or other computer technology, to collect the effective information in the image, and finally generate the image with the largest amount of information. Under the same target, multiple different source images are fused by the operator or neural network to form a new image with multiple information.…”

Section: Introductionmentioning

confidence: 99%

Image fusion algorithm in Integrated Space-Ground-Sea Wireless Networks of B5G

Cui

Wang

et al. 2021

EURASIP J. Adv. Signal Process.

View full text Add to dashboard Cite

In recent years, in Space-Ground-Sea Wireless Networks, the rapid development of image recognition also promotes the development of images fusion. For example, the content of a single-mode medical image is very single, and the fused image contains more image information, which provides a more reliable basis for diagnosis. However, in wireless communication and medical image processing, the image fusion effect is poor and the efficiency is low. To solve this problem, an image fusion algorithm based on fast finite shear wave transform and convolutional neural network is proposed for wireless communication in this paper. This algorithm adopts the methods such as fast finite shear wave transform (FFST), reducing the dimension of the convolution layer, and the inverse process of fast finite shear wave transform. The experimental results show that the algorithm has a very good effect in both objective indicators and subjective vision, and it is also very feasible in wireless communication.

show abstract

The adaptive finite element method for the P-Laplace problem

Cited by 6 publications

References 21 publications

Explicit and efficient error estimation for convex minimization problems

Explicit and efficient error estimation for convex minimization problems

Image Fusion Algorithm in Integrated Space-Ground-Sea Wireless Networks of B5G

Image fusion algorithm in Integrated Space-Ground-Sea Wireless Networks of B5G

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