This work is concerned with time stepping finite element methods for abstract second order evolution problems. We derive optimal order a posteriori error estimates and a posteriori nodal superconvergence error estimat...This work is concerned with time stepping finite element methods for abstract second order evolution problems. We derive optimal order a posteriori error estimates and a posteriori nodal superconvergence error estimates using the energy approach and the duality argument. With the help of the a posteriori error estimator developed in this work, we will further propose an adaptive time stepping strategy. A number of numerical experiments are performed to illustrate the reliability and efficiency of the a posteriori error estimates and to assess the effectiveness of the proposed adaptive time stepping method.展开更多
Control policies such as "odd-and-even license plate rule" were implemented by the Chinese government to restrict traffic and suspend factory production in Beijing and neighboring cities during the Asia-Paci...Control policies such as "odd-and-even license plate rule" were implemented by the Chinese government to restrict traffic and suspend factory production in Beijing and neighboring cities during the Asia-Pacific Economic Cooperation summit. We use ozone monitoring instrument(OMI), mobile differential optical absorption spectroscopy(DOAS), and multi-axis differential optical absorption spectroscopy(MAX-DOAS) to measure the variation of the spatial and temporal patterns of NO2 column densities from October 24, 2014 to November 22, 2014. It is found that the NO2 column densities during the episode of control policies are significantly lower than those during other periods, and the emission flux of NO2 calculated by mobile DOAS is also lower than the results from other periods. Some daily low NO2 column densities occur with the northwest wind direction. We then compare the relationship between OMI and mobile DOAS NO2 column density observations, and the results of mobile DOAS are approximately 2.7 times larger than the OMI values. The largest discrepancy occurs in the northern part of Beijing city. In other parts, the two instruments have a better correlation coefficient(R2) of 0.61. The low NO2 column densities that occur during the episode of control policies are affected by the control policies as well as meteorological conditions.展开更多
基金supported by National Natural Science Foundation of China(Grant Nos.1117121911161130004 and 11101199)+1 种基金E-Institutes of Shanghai Municipal Education Commission(Grant No.E03004)Program for New Century Excellent Talents in Fujian Province University(Grant No.JA12260)
文摘This work is concerned with time stepping finite element methods for abstract second order evolution problems. We derive optimal order a posteriori error estimates and a posteriori nodal superconvergence error estimates using the energy approach and the duality argument. With the help of the a posteriori error estimator developed in this work, we will further propose an adaptive time stepping strategy. A number of numerical experiments are performed to illustrate the reliability and efficiency of the a posteriori error estimates and to assess the effectiveness of the proposed adaptive time stepping method.
基金supported by the National Natural Science Foundation of China(41275038)the Key Research Program of the Chinese Academy of Sciences(KJZD-EW-TZ-G06)+2 种基金the National High Technology Research and Development Program of China(2014AA06A508,2014AA06A511)the Scientific and Technological Project of Anhui Province(1301022083)the Special Project of Environmental Nonprofit Industry Research,China(201409006)
文摘Control policies such as "odd-and-even license plate rule" were implemented by the Chinese government to restrict traffic and suspend factory production in Beijing and neighboring cities during the Asia-Pacific Economic Cooperation summit. We use ozone monitoring instrument(OMI), mobile differential optical absorption spectroscopy(DOAS), and multi-axis differential optical absorption spectroscopy(MAX-DOAS) to measure the variation of the spatial and temporal patterns of NO2 column densities from October 24, 2014 to November 22, 2014. It is found that the NO2 column densities during the episode of control policies are significantly lower than those during other periods, and the emission flux of NO2 calculated by mobile DOAS is also lower than the results from other periods. Some daily low NO2 column densities occur with the northwest wind direction. We then compare the relationship between OMI and mobile DOAS NO2 column density observations, and the results of mobile DOAS are approximately 2.7 times larger than the OMI values. The largest discrepancy occurs in the northern part of Beijing city. In other parts, the two instruments have a better correlation coefficient(R2) of 0.61. The low NO2 column densities that occur during the episode of control policies are affected by the control policies as well as meteorological conditions.
