This paper is concerned with the L^p-L^q estimates of the solutions for a class of pseudodifferential equations under some suitable degenerate assumptions. As applications, these estimates can be used to show that a g...This paper is concerned with the L^p-L^q estimates of the solutions for a class of pseudodifferential equations under some suitable degenerate assumptions. As applications, these estimates can be used to show that a generalized Schroedinger operator with some integrable potential generates a fractionally integrated group in L^p（R^n）.展开更多
Adaptive methods have been rapidly developed and applied in many fields of scientific and engi- neering computing. Reliable and efficient a posteriori error estimates play key roles for both adaptive finite element ...Adaptive methods have been rapidly developed and applied in many fields of scientific and engi- neering computing. Reliable and efficient a posteriori error estimates play key roles for both adaptive finite element and boundary element methods. The aim of this paper is to develop a posteriori error estimates for boundary element methods. The standard a posteriori error estimates for boundary element methods are obtained from the classical boundary integral equations. This paper presents hyper-singular a posteriori er- ror estimates based on the hyper-singular integral equations. Three kinds of residuals are used as the esti- mates for boundary element errors. The theoretical analysis and numerical examples show that the hyper- singular residuals are good a posteriori error indicators in many adaptive boundary element computations.展开更多
基金Supported by National Natural Science Foundation of China （Grant No. 10801057）, Key Project of Chinese Ministry of Education （Grant No. 109117） and CCNU Project （Grant No. CCNU09A02015）
文摘This paper is concerned with the L^p-L^q estimates of the solutions for a class of pseudodifferential equations under some suitable degenerate assumptions. As applications, these estimates can be used to show that a generalized Schroedinger operator with some integrable potential generates a fractionally integrated group in L^p（R^n）.
基金Supported by the National Key Basic Research and Development(973) Program of China (No. G19990328) and the Knowledge Innovation Program of the Chinese Academy of Sciences
文摘Adaptive methods have been rapidly developed and applied in many fields of scientific and engi- neering computing. Reliable and efficient a posteriori error estimates play key roles for both adaptive finite element and boundary element methods. The aim of this paper is to develop a posteriori error estimates for boundary element methods. The standard a posteriori error estimates for boundary element methods are obtained from the classical boundary integral equations. This paper presents hyper-singular a posteriori er- ror estimates based on the hyper-singular integral equations. Three kinds of residuals are used as the esti- mates for boundary element errors. The theoretical analysis and numerical examples show that the hyper- singular residuals are good a posteriori error indicators in many adaptive boundary element computations.
