The superconvergence in the finite element method is a phenomenon in which the fi-nite element approximation converges to the exact solution at a rate higher than the optimal order error estimate. Wang proposed and an...The superconvergence in the finite element method is a phenomenon in which the fi-nite element approximation converges to the exact solution at a rate higher than the optimal order error estimate. Wang proposed and analyzed superconvergence of the conforming finite element method by L2-projections. However, since the conforming finite element method (CFEM) requires a strong continuity, it is not easy to construct such finite elements for the complex partial differential equations. Thus, the nonconforming finite element method (NCFEM) is more appealing computationally due to better stability and flexibility properties compared to CFEM. The objective of this paper is to establish a general superconvergence result for the nonconforming finite element approximations for second-order elliptic problems by L2-projection methods by applying the idea presented in Wang. MATLAB codes are published at https://github.com/annaleeharris/Superconvergence-NCFEM for anyone to use and to study. The results of numerical experiments show great promise for the robustness, reliability, flexibility and accuracy of superconvergence in NCFEM by L2- projections.展开更多
The superconvergence in the finite element method is a phenomenon in which the finite element approximation converges to the exact solution at a rate higher than the optimal order error estimate. Wang proposed and ana...The superconvergence in the finite element method is a phenomenon in which the finite element approximation converges to the exact solution at a rate higher than the optimal order error estimate. Wang proposed and analyzed superconvergence of the conforming finite element method by L2-projections. The goal of this paper is to perform numerical experiments using MATLAB to support and to verify the theoretical results in Wang for the superconvergence of the conforming finite element method (CFEM) for the second order elliptic problems by L2-projection methods. MATLAB codes are published at https://github.com/annaleeharris/Superconvergence-CFEM for anyone to use and to study.展开更多
A Mobile Ad Hoc Network (MANET) is a self-governing network of mobile nodes without the inclusion of any wired links. Each node can move in an ad hoc manner and therefore, such a network should consist of routing prot...A Mobile Ad Hoc Network (MANET) is a self-governing network of mobile nodes without the inclusion of any wired links. Each node can move in an ad hoc manner and therefore, such a network should consist of routing protocols which can adapt to dynamically changing topologies. Numerous protocols have been proposed for the same. However, the trajectories followed by the individual nodes have not been distinctly dealt with. This paper presents a meticulous study on QoS parameters of proactive (OLSR) and reactive (DSR) protocols of MANETs for uniform as well as dissimilar trajectories of individual nodes in a small network of about 20 nodes. Also an examination of partial node failures for both the above mentioned protocols has been done. The performance metrics utilized in this study are average throughput and average delay. OPNET modeler has been utilized for this study. This assessment shows that for uniform trajectories, OLSR has almost same average delay but a higher average throughput as compared to DSR. Also it is seen that, as compared to uniform trajectories, non-uniform trajectories deliver a much higher average throughput. Node failures only reduce average throughputs whereas average delays remain unchanged.展开更多
Traumatic neuroma is a well-recognized complication of lower extremity amputation,yet has also been noted to occur elsewhere.We report a clinical case and English-language literature review of traumatic rectal neuroma...Traumatic neuroma is a well-recognized complication of lower extremity amputation,yet has also been noted to occur elsewhere.We report a clinical case and English-language literature review of traumatic rectal neuroma,a well-known pathologic entity not previously reported in this anatomic location.展开更多
文摘The superconvergence in the finite element method is a phenomenon in which the fi-nite element approximation converges to the exact solution at a rate higher than the optimal order error estimate. Wang proposed and analyzed superconvergence of the conforming finite element method by L2-projections. However, since the conforming finite element method (CFEM) requires a strong continuity, it is not easy to construct such finite elements for the complex partial differential equations. Thus, the nonconforming finite element method (NCFEM) is more appealing computationally due to better stability and flexibility properties compared to CFEM. The objective of this paper is to establish a general superconvergence result for the nonconforming finite element approximations for second-order elliptic problems by L2-projection methods by applying the idea presented in Wang. MATLAB codes are published at https://github.com/annaleeharris/Superconvergence-NCFEM for anyone to use and to study. The results of numerical experiments show great promise for the robustness, reliability, flexibility and accuracy of superconvergence in NCFEM by L2- projections.
文摘The superconvergence in the finite element method is a phenomenon in which the finite element approximation converges to the exact solution at a rate higher than the optimal order error estimate. Wang proposed and analyzed superconvergence of the conforming finite element method by L2-projections. The goal of this paper is to perform numerical experiments using MATLAB to support and to verify the theoretical results in Wang for the superconvergence of the conforming finite element method (CFEM) for the second order elliptic problems by L2-projection methods. MATLAB codes are published at https://github.com/annaleeharris/Superconvergence-CFEM for anyone to use and to study.
文摘A Mobile Ad Hoc Network (MANET) is a self-governing network of mobile nodes without the inclusion of any wired links. Each node can move in an ad hoc manner and therefore, such a network should consist of routing protocols which can adapt to dynamically changing topologies. Numerous protocols have been proposed for the same. However, the trajectories followed by the individual nodes have not been distinctly dealt with. This paper presents a meticulous study on QoS parameters of proactive (OLSR) and reactive (DSR) protocols of MANETs for uniform as well as dissimilar trajectories of individual nodes in a small network of about 20 nodes. Also an examination of partial node failures for both the above mentioned protocols has been done. The performance metrics utilized in this study are average throughput and average delay. OPNET modeler has been utilized for this study. This assessment shows that for uniform trajectories, OLSR has almost same average delay but a higher average throughput as compared to DSR. Also it is seen that, as compared to uniform trajectories, non-uniform trajectories deliver a much higher average throughput. Node failures only reduce average throughputs whereas average delays remain unchanged.
文摘Traumatic neuroma is a well-recognized complication of lower extremity amputation,yet has also been noted to occur elsewhere.We report a clinical case and English-language literature review of traumatic rectal neuroma,a well-known pathologic entity not previously reported in this anatomic location.
