Superconvergence of semidiscrete finite element methods for bilinear parabolic optimal control problems

Abstract In this paper, a semidiscrete finite element method for solving bilinear parabolic optimal control problems is considered. Firstly, we present a finite element approximation of the model problem. Secondly, we bring in some important intermediate variables and their error estimates. Thirdly, we derive a priori error estimates of the approximation scheme. Finally, we obtain the superconvergence between the semidiscrete finite element solutions and projections of the exact solutions. A numerical example is presented to verify our theoretical results

Error estimates of mixed finite elements combined with Crank-Nicolson scheme for parabolic control problems

In this paper, a mixed finite element method combined with Crank-Nicolson scheme approximation of parabolic optimal control problems with control constraint is investigated. For the state and co-state, the order Raviart-Thomas mixed finite element spaces and Crank-Nicolson scheme are used for space and time discretization, respectively. The variational discretization technique is used for the control variable. We derive optimal priori error estimates for the control, state and co-state. Some numerical examples are presented to demonstrate the theoretical results

An improved finite element approximation and superconvergence for temperature control problems

In this paper, we consider an improved finite element approximation for temperature control problems, where the state and the adjoint state are discretized by piecewise linear functions while the control is not discretized directly. The numerical solution of the control is obtained by a projection of the adjoint state to the set of admissible controls. We derive a priori error estimates and superconvergence of second-order. Moreover, we present some numerical examples to illustrate our theoretical results

Sequential Reassortments Underlie Diverse Influenza H7N9 Genotypes in China

Initial genetic characterizations have suggested that the influenza A (H7N9) viruses responsible for the current outbreak in China are novel reassortants. However, little is known about the pathways of their evolution and, in particular, the generation of diverse viral genotypes. Here we report an in-depth evolutionary analysis of whole-genome sequence data of 45 H7N9 and 42 H9N2 viruses isolated from humans, poultry, and wild birds during recent influenza surveillance efforts in China. Our analysis shows that the H7N9 viruses were generated by at least two steps of sequential reassortments involving distinct H9N2 donor viruses in different hosts. The first reassortment likely occurred in wild birds and the second in domestic birds in east China in early 2012. Our study identifies the pathways for the generation of diverse H7N9 genotypes in China and highlights the importance of monitoring multiple sources for effective surveillance of potential influenza outbreaks.National Natural Science Foundation (China) (31125016)National Natural Science Foundation (China) (31371338)National Center for Biotechnology Information (U.S.) (Major National Earmark Project for Infectious Diseases, 2013ZX10004611-002)National Basic Research Program of China (973 Program)National Basic Research Program of China (973 Program, grant, 2009CB918503)National Science and Technology Major Projects (2012ZX10004214001002)Jiangsu Sheng (China) (Priority Academic Program Development of Jiangsu Higher Education Institutions)National Natural Science Foundation (China) (31100950)MIT International Science and Technology Initiative

Spatiotemporal Genotype Replacement of H5N8 Avian Influenza Viruses Contributed to H5N1 Emergence in 2021/2022 Panzootic

Since 2020, clade 2.3.4.4b highly pathogenic avian influenza H5N8 and H5N1 viruses have swept through continents, posing serious threats to the world. Through comprehensive analyses of epidemiological, genetic, and bird migration data, we found that the dominant genotype replacement of the H5N8 viruses in 2020 contributed to the H5N1 outbreak in the 2021/2022 wave. The 2020 outbreak of the H5N8 G1 genotype instead of the G0 genotype produced reassortment opportunities and led to the emergence of a new H5N1 virus with G1's HA and MP genes. Despite extensive reassortments in the 2021/2022 wave, the H5N1 virus retained the HA and MP genes, causing a significant outbreak in Europe and North America. Furtherly, through the wild bird migration flyways investigation, we found that the temporal-spatial coincidence between the outbreak of the H5N8 G1 virus and the bird autumn migration may have expanded the H5 viral spread, which may be one of the main drivers of the emergence of the 2020-2022 H5 panzootic.IMPORTANCESince 2020, highly pathogenic avian influenza (HPAI) H5 subtype variants of clade 2.3.4.4b have spread across continents, posing unprecedented threats globally. However, the factors promoting the genesis and spread of H5 HPAI viruses remain unclear. Here, we found that the spatiotemporal genotype replacement of H5N8 HPAI viruses contributed to the emergence of the H5N1 variant that caused the 2021/2022 panzootic, and the viral evolution in poultry of Egypt and surrounding area and autumn bird migration from the Russia-Kazakhstan region to Europe are important drivers of the emergence of the 2020-2022 H5 panzootic. These findings provide important targets for early warning and could help control the current and future HPAI epidemics.</p

Interpolated Coefficient Mixed Finite Elements for Semilinear Time Fractional Diffusion Equations

In this paper, we consider a fully discrete interpolated coefficient mixed finite element method for semilinear time fractional reaction–diffusion equations. The classic L1 scheme based on graded meshes and new mixed finite element based on triangulation is used for the temporal and spatial discretization, respectively. The interpolation coefficient technique is used to deal with the semilinear term, and the discrete nonlinear system is solved by a Newton-like iterative method. Stability and convergence results for both the original variable and its flux are derived. Numerical experiments confirm our theoretical analysis

Interpolated coefficient characteristic finite element method for semilinear convection–diffusion optimal control problems

In this paper, a fully discrete interpolated coefficient characteristic finite element approximation is proposed for optimal control problems governed by time-dependent semilinear convection–diffusion equations, where the hyperbolic part of the state equation is first treated by directional derivatives and then discretized by backward difference, the semilinear term is dealt with interpolation coefficient finite elements technique. A priori error estimates for the control, state and co-state variables are derived. Theoretic results are confirmed by a numerical example