In this paper,we analyze a class of globally divergence-free(and therefore pressure-robust)hybridizable discontinuous Galerkin(HDG)finite element methods for stationary Navier-Stokes equations.The methods use the P_(k...In this paper,we analyze a class of globally divergence-free(and therefore pressure-robust)hybridizable discontinuous Galerkin(HDG)finite element methods for stationary Navier-Stokes equations.The methods use the P_(k)/P_(k-1)(k≥1)discontinuous finite element combination for the velocity and pressure approximations in the interior of elements,piecewise Pm(m=k,k-1)for the velocity gradient approximation in the interior of elements,and piecewise P_(k)/P_(k) for the trace approximations of the velocity and pressure on the inter-element boundaries.We show that the uniqueness condition for the discrete solution is guaranteed by that for the continuous solution together with a sufficiently small mesh size.Based on the derived discrete HDG Sobolev embedding properties,optimal error estimates are obtained.Numerical experiments are performed to verify the theoretical analysis.展开更多
Root architecture is crucial for plants to absorb water and nutrients. We previously reported edtl （edtlD） mutant with altered root architecture that contributes significantly to drought resistance. However, the und...Root architecture is crucial for plants to absorb water and nutrients. We previously reported edtl （edtlD） mutant with altered root architecture that contributes significantly to drought resistance. However, the underlying molecular mechanisms are not well understood. Here we report one of the mechanisms underlying EDT1/HDGll- conferred altered root architecture. Root transcriptome comparison between the wild type and edtlD revealed that the upregulated genes involved in jasmonate biosynthesis and signaling pathway were enriched in edtlD root, which were confirmed by quantitative RT-PCR. Further analysis showed that EDT1/HDG11, as a transcription factor, bound directly to the HD binding sites in the promoters of AOS, AOC3, OPR3, and OPCL1, which encode four key enzymes in JA biosynthesis. We found that the jasmonic acid level was significantly elevated in edtlD root compared with that in the wild type subsequently. In addition, more auxin accumulation was observed in thelateral root primordium of edtlD compared with that of wild type. Genetic analysis of edtlD opcl1 double mutant also showed that HDGll was partially dependent on JA in regulating LR formation. Taken together, overexpression of EDT1/HDGll increases JA level in the root of edtlD by directly upregulating the expressions of several genes encoding JA biosynthesis enzymes to activate auxin signaling and promote lateral root formation.展开更多
A new second order time stepping ensemble hybridizable discontinuous Galerkin method for parameterized convection diffusion PDEs with various initial and boundary conditions,body forces,and time depending coefficients...A new second order time stepping ensemble hybridizable discontinuous Galerkin method for parameterized convection diffusion PDEs with various initial and boundary conditions,body forces,and time depending coefficients is developed.For ensemble solutions in L_(∞)(0,T;L^(2)(Ω)),a superconvergent rate with respect to the freedom degree of the globally coupled unknowns for all the polynomials of degree k≥0 is established.The results of numerical experiments are consistent with the theoretical findings.展开更多
The purpose of this paper is to develop a hybridized discontinuous Galerkin(HDG)method for solving the Ito-type coupled KdV system.In fact,we use the HDG method for discre-tizing the space variable and the backward Eu...The purpose of this paper is to develop a hybridized discontinuous Galerkin(HDG)method for solving the Ito-type coupled KdV system.In fact,we use the HDG method for discre-tizing the space variable and the backward Euler explicit method for the time variable.To linearize the system,the time-lagging approach is also applied.The numerical stability of the method in the sense of the L2 norm is proved using the energy method under certain assumptions on the stabilization parameters for periodic or homogeneous Dirichlet bound-ary conditions.Numerical experiments confirm that the HDG method is capable of solving the system efficiently.It is observed that the best possible rate of convergence is achieved by the HDG method.Also,it is being illustrated numerically that the corresponding con-servation laws are satisfied for the approximate solutions of the Ito-type coupled KdV sys-tem.Thanks to the numerical experiments,it is verified that the HDG method could be more efficient than the LDG method for solving some Ito-type coupled KdV systems by comparing the corresponding computational costs and orders of convergence.展开更多
基金supported by National Natural Science Foundation of China(Grant Nos.12171341 and 11801063)supported by National Natural Science Foundation of China(Grant Nos.12171340 and 11771312)the Fundamental Research Funds for the Central Universities(Grant No.YJ202030)。
文摘In this paper,we analyze a class of globally divergence-free(and therefore pressure-robust)hybridizable discontinuous Galerkin(HDG)finite element methods for stationary Navier-Stokes equations.The methods use the P_(k)/P_(k-1)(k≥1)discontinuous finite element combination for the velocity and pressure approximations in the interior of elements,piecewise Pm(m=k,k-1)for the velocity gradient approximation in the interior of elements,and piecewise P_(k)/P_(k) for the trace approximations of the velocity and pressure on the inter-element boundaries.We show that the uniqueness condition for the discrete solution is guaranteed by that for the continuous solution together with a sufficiently small mesh size.Based on the derived discrete HDG Sobolev embedding properties,optimal error estimates are obtained.Numerical experiments are performed to verify the theoretical analysis.
基金supported by grants from the Ministry of Science and Technology of China (MOST, 2012CB114304, 2011ZX08005-004)the Chinese Academy of Science (CAS, KSCX3-YW-N-007)the National Nature Science Foundation of China (NNSFC, 30830075, 90917004)
文摘Root architecture is crucial for plants to absorb water and nutrients. We previously reported edtl （edtlD） mutant with altered root architecture that contributes significantly to drought resistance. However, the underlying molecular mechanisms are not well understood. Here we report one of the mechanisms underlying EDT1/HDGll- conferred altered root architecture. Root transcriptome comparison between the wild type and edtlD revealed that the upregulated genes involved in jasmonate biosynthesis and signaling pathway were enriched in edtlD root, which were confirmed by quantitative RT-PCR. Further analysis showed that EDT1/HDG11, as a transcription factor, bound directly to the HD binding sites in the promoters of AOS, AOC3, OPR3, and OPCL1, which encode four key enzymes in JA biosynthesis. We found that the jasmonic acid level was significantly elevated in edtlD root compared with that in the wild type subsequently. In addition, more auxin accumulation was observed in thelateral root primordium of edtlD compared with that of wild type. Genetic analysis of edtlD opcl1 double mutant also showed that HDGll was partially dependent on JA in regulating LR formation. Taken together, overexpression of EDT1/HDGll increases JA level in the root of edtlD by directly upregulating the expressions of several genes encoding JA biosynthesis enzymes to activate auxin signaling and promote lateral root formation.
基金G.Chen was supported by National Natural Science Foundation of China(NSFC)(11801063)by China Postdoctoral Science Foundation(2018M633339,2019T120808)+1 种基金by the Fundamental Research Funds for the Central Universities(YJ202030)Y.Zhang was supported by US National Science Foundation(NSF)(DMS-1619904).
文摘A new second order time stepping ensemble hybridizable discontinuous Galerkin method for parameterized convection diffusion PDEs with various initial and boundary conditions,body forces,and time depending coefficients is developed.For ensemble solutions in L_(∞)(0,T;L^(2)(Ω)),a superconvergent rate with respect to the freedom degree of the globally coupled unknowns for all the polynomials of degree k≥0 is established.The results of numerical experiments are consistent with the theoretical findings.
文摘The purpose of this paper is to develop a hybridized discontinuous Galerkin(HDG)method for solving the Ito-type coupled KdV system.In fact,we use the HDG method for discre-tizing the space variable and the backward Euler explicit method for the time variable.To linearize the system,the time-lagging approach is also applied.The numerical stability of the method in the sense of the L2 norm is proved using the energy method under certain assumptions on the stabilization parameters for periodic or homogeneous Dirichlet bound-ary conditions.Numerical experiments confirm that the HDG method is capable of solving the system efficiently.It is observed that the best possible rate of convergence is achieved by the HDG method.Also,it is being illustrated numerically that the corresponding con-servation laws are satisfied for the approximate solutions of the Ito-type coupled KdV sys-tem.Thanks to the numerical experiments,it is verified that the HDG method could be more efficient than the LDG method for solving some Ito-type coupled KdV systems by comparing the corresponding computational costs and orders of convergence.
