We prove that the error estimates of a large class of nonconforming finite elements are dominated by their approximation errors, which means that the well-known Cea’s lemma is still valid for these nonconforming fini...
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We prove that the error estimates of a large class of nonconforming finite elements are dominated by their approximation errors, which means that the well-known Cea’s lemma is still valid for these nonconforming finite element methods. Furthermore, we derive the error estimates in both energy and L2 norms under the regularity assumption u ∈ H1+s(Ω) with any s > 0. The extensions to other related problems are possible.
Modeling of biomolecular systems plays an essential role in understanding biological processes, such as ionic flow across channels, protein modification or interaction, and cell signaling. The continuum model describe...
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Modeling of biomolecular systems plays an essential role in understanding biological processes, such as ionic flow across channels, protein modification or interaction, and cell signaling. The continuum model described by the Poisson- Boltzmann （PB）/Poisson-Nernst-Planck （PNP） equations has made great contributions towards simulation of these pro- cesses. However, the model has shortcomings in its commonly used form and cannot capture （or cannot accurately capture） some important physical properties of the biological systems. Considerable efforts have been made to improve the con- tinuum model to account for discrete particle interactions and to make progress in numerical methods to provide accurate and efficient simulations. This review will summarize recent main improvements in continuum modeling for biomolecu- lar systems, with focus on the size-modified models, the coupling of the classical density functional theory and the PNP equations, the coupling of polar and nonpolar interactions, and numerical progress.
A class of hybrid algebraic multilevel preconditioning methods is presented for solving systems of linear equations with symmetric positive-definite matrices resulting from the discretization of many second-order elli...
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A class of hybrid algebraic multilevel preconditioning methods is presented for solving systems of linear equations with symmetric positive-definite matrices resulting from the discretization of many second-order elliptic boundary value problems by the finite element method. The new preconditioners are shown to be of optimal orders of complexities for 2-D and 3-D problem domains, and their relative condition numbers are estimated to be bounded uniformly with respect to the numbers of both levels and nodes.
Human pose estimation in videos remains a challenge, largely due to the reliance on extensive manual annotation of large datasets, which is expensive and labor-intensive. Furthermore, existing approaches often struggl...
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Human pose estimation has given rise to a broad spectrum of novel and compelling applications, including action recognition, sports analysis, as well as surveillance. However, accurate video pose estimation remains an...
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Examines a nonoverlapping domain decomposition method based on the natural boundary reduction. Development of the D-N alternating algorithm; Studies the convergence of the D-N method for exterior spherical domain; Dis...
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Examines a nonoverlapping domain decomposition method based on the natural boundary reduction. Development of the D-N alternating algorithm; Studies the convergence of the D-N method for exterior spherical domain; Discussion of the discrete form of the D-N alternating algorithm.
Recent advancements in model pruning have focused on developing new algorithms and improving upon benchmarks. However, the practical application of these algorithms across various models and platforms remains a signif...
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A new comparison theorem on the monotone convergence rates of the parallel nonlinear multisplitting accelerated overrelaxation (AOR) method for solving the large scale nonlinear complementarity problem is established....
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A new comparison theorem on the monotone convergence rates of the parallel nonlinear multisplitting accelerated overrelaxation (AOR) method for solving the large scale nonlinear complementarity problem is established. Thus, the monotone convergence theory of this class of method is completed.
Sequential pattern mining (SPM) with gap constraints (or repetitive SPM or tandem repeat discovery in bioinformatics) can find frequent repetitive subsequences satisfying gap constraints, which are called positive seq...
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To reduce computational cost,we study some two-scale finite element approximations on sparse grids for elliptic partial differential equations of second order in a general *** any tensor product domain ?R^d with d =...
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To reduce computational cost,we study some two-scale finite element approximations on sparse grids for elliptic partial differential equations of second order in a general *** any tensor product domain ?R^d with d = 2,3,we construct the two-scale finite element approximations for both boundary value and eigenvalue problems by using a Boolean sum of some existing finite element approximations on a coarse grid and some univariate fine grids and hence they are cheaper *** applications,we obtain some new efficient finite element discretizations for the two classes of problem:The new two-scale finite element approximation on a sparse grid not only has the less degrees of freedom but also achieves a good accuracy of approximation.
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