Collapse is a common geomorphic process in karst areas,especially on the Yunnan-Guizhou Plateau,which has a tectonic background of integral uplift.The frequent occurrence of collapse processes in karst underground cav...Collapse is a common geomorphic process in karst areas,especially on the Yunnan-Guizhou Plateau,which has a tectonic background of integral uplift.The frequent occurrence of collapse processes in karst underground caves and canyons indicates that collapses play an important role in the formation of canyons.Through an analysis of the morphology of a semicircular cliff in the Huajiang Grand Canyon and an investigation of sediments at the bottom of the cliff,a large-scale collapse event was found to have occurred.U-series dating of secondary calcium carbonate cement in the collapse breccias indicates that collapse processes occurred approximately 200 ka.According to the geomorphological evolution of the Huajiang Grand Canyon,the following geomorphic evolutionary process is proposed:underground river-cave hall-collapse of a tiankeng-tiankeng degradation-canyon formation.These findings also show that the dating of collapsed breccia cement can be effectively used to determine the development times of karst canyons and the formation ages of tiankengs.展开更多
In this paper we introduce a Petrov-Galerkin approximation model to the solution of linear and semi-linear elliptic boundary value problems in which piecewise quadratic polynomial space and piecewise linear polynomial...In this paper we introduce a Petrov-Galerkin approximation model to the solution of linear and semi-linear elliptic boundary value problems in which piecewise quadratic polynomial space and piecewise linear polynomial space are used as the shape function space and the test function space, respectively. We prove that the approximation order of the standard quadratic finite element can be attained in this Petrov-Galerkin model. Based on the so-called 'contractivity' of the interpolation operator, we further prove that the defect iterative sequence of the linear finite element solution converge to the proposed Petrov-Galerkin approximate solution.展开更多
基金funded by the National Natural Science Foundation of China(Grant Nos:42061001,41501006)The Science and Technology Foundation of Guizhou Province(Grant Nos:Qianke Jichu-ZK[2021]190)Natural science research funding project of Guizhou Provincial Department of Education(Grant No.:Qian Jiao KY[2021]036).
文摘Collapse is a common geomorphic process in karst areas,especially on the Yunnan-Guizhou Plateau,which has a tectonic background of integral uplift.The frequent occurrence of collapse processes in karst underground caves and canyons indicates that collapses play an important role in the formation of canyons.Through an analysis of the morphology of a semicircular cliff in the Huajiang Grand Canyon and an investigation of sediments at the bottom of the cliff,a large-scale collapse event was found to have occurred.U-series dating of secondary calcium carbonate cement in the collapse breccias indicates that collapse processes occurred approximately 200 ka.According to the geomorphological evolution of the Huajiang Grand Canyon,the following geomorphic evolutionary process is proposed:underground river-cave hall-collapse of a tiankeng-tiankeng degradation-canyon formation.These findings also show that the dating of collapsed breccia cement can be effectively used to determine the development times of karst canyons and the formation ages of tiankengs.
文摘In this paper we introduce a Petrov-Galerkin approximation model to the solution of linear and semi-linear elliptic boundary value problems in which piecewise quadratic polynomial space and piecewise linear polynomial space are used as the shape function space and the test function space, respectively. We prove that the approximation order of the standard quadratic finite element can be attained in this Petrov-Galerkin model. Based on the so-called 'contractivity' of the interpolation operator, we further prove that the defect iterative sequence of the linear finite element solution converge to the proposed Petrov-Galerkin approximate solution.
