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We devise and analyze |$C^0$| -conforming hybrid high-order (HHO) methods to approximate biharmonic problems with either clamped or simply supported boundary conditions. |$C^0$| -conforming HHO methods hinge on cell unknowns that are |$C^0$| -conforming polynomials of order |$(k+2)$| approximating the solution in the mesh cells and on face unknowns, which are polynomials of order |$k\ge 0$| approximating the normal derivative of the solution on the mesh skeleton. Such methods deliver |$O(h^{k+1})$| |$H^2$| -error estimates for smooth solutions. An important novelty in the error analysis is to lower the minimal regularity requirement on the exact solution. The technique to achieve this has a broader applicability than just |$C^0$| -conforming HHO methods, and to illustrate this point, we outline the error analysis for the well-known |$C^0$| -conforming interior penalty discontinuous Galerkin methods as well. The present technique does not require a |$C^1$| -smoother to evaluate the right-hand side in case of rough loads; loads in |$W^{-1,q}$|⁠ , |$q>\frac {2d}{d+2}$|⁠ , are covered, but not in |$H^{-2}$|⁠. Finally, numerical results including comparisons to various existing methods showcase the efficiency of the proposed |$C^0$| -conforming HHO methods. [ABSTRACT FROM AUTHOR]

Low-dose CT images contain severe mottle noise and streak artifacts, which seriously affect the physician’s diagnosis of the disease. Hence, in this paper, we propose a novel anisotropic fourth-order diffusion model for low-dose CT image processing. The proposed diffusion model uses both image gradient magnitude and weighted residual local energy to determine the diffusion coefficient. Gradient magnitude is used to detect the image edges, while the weighted residual local energy preserves textures and details in the image. In addition, the fidelity term is introduced into the diffusion model to avoid excessive smoothing and weaken the blocky effects. Experimental results show that when compared with the anisotropic fourth-order diffusion model, the proposed algorithm protects the texture details and suppresses the blocky effects. In comparison with other state-of-the-art algorithms, the proposed model effectively suppresses mottle noise and streak artifacts while simultaneously improving the low-dose CT image quality.

We devise and analyze two hybrid high-order (HHO) methods for the numerical approximation of the biharmonic problem. The methods support polyhedral meshes, rely on the primal formulation of the problem, and deliver O(hk+1) H²-error estimates when using polynomials of order k ≥ 0 to approximate the normal derivative on the mesh (inter)faces. Both HHO methods hinge on a stabilization in the spirit of Lehrenfeld and Sch\"oberl for second-order PDEs. The cell unknowns are polynomials of order (k+2) that can be eliminated locally by means of static condensation. The face unknowns approximating the trace of the solution on the mesh (inter)faces are polynomials of order (k + 1) in the first HHO method, which is valid in dimension two and uses an original stabilization involving the canonical hybrid finite element, and they are of order (k + 2) for the second HHO method, which is valid in arbitrary dimension and uses only L²-orthogonal projections in the stabilization. A comparative discussion with the weak Galerkin methods from the literature is provided, highlighting the close connections and the improvements proposed herein. Additionally, we show how the two HHO methods can be combined with a Nitsche-like boundary-penalty technique to weakly enforce the boundary conditions. An originality in the devised Nitsche's technique is to avoid any penalty parameter that must be large enough. Finally, numerical results showcase the efficiency of the proposed methods and indicate that the HHO methods can generally outperform discontinuous Galerkin methods and even be competitive with C0-interior penalty methods on triangular meshes. [ABSTRACT FROM AUTHOR]