Determining the optimal biomass of macrophytes during the ecological restoration process of eutrophic shallow lakes

Many studies have shown that macrophytes play a significant role in controlling eutrophication; however, only a few of these are based on macrophyte biomass. Based on the growth characteristic of macrophytes, we propose an approach for the assessment of the optimal biomass of macrophytes in the decay and growth periods in Lake Datong (a shallow lake), using a lake ecological model. The results showed that the pollution load of the lake should be reduced by 50% while conforming to the Environmental Quality Standards for Surface Water (EQSSW) Class Ⅲ. In contrast, with an increase in the pollution load of 5%, the results indicate that the lake may deteriorate to a turbid state over the next few years. The macrophyte biomass should be harvested during the decay period, when 80% biomass is beneficial to the water quality of the eutrophic shallow lake. Based on macrophyte simulation from 2020–2024, the wet biomass of macrophytes should be controlled at 5.5 kg/m2. The current macrophyte biomass in Lake Datong is four-fold higher than the simulated optimal biomass. This study provides a reference for the adequate ecological restoration of the lake and its subsequent maintenance, as well as scientific support for improving the comprehensive evaluation standard of healthy lakes and the theoretical basis of lake ecological restoration

Finite element pressure stabilizations for incompressible flow problems

Discretizations of incompressible flow problems with pairs of finite element spaces that do not satisfy a discrete inf-sup condition require a so-called pressure stabilization. This paper gives an overview and systematic assessment of stabilized methods, including the respective error analysis

An L"2- and L"0"0-error analysis for parabolic finite element equations with applications to superconvergence and error expansions

SIGLEAvailable from TIB Hannover: RR 1606(93-11) / FIZ - Fachinformationszzentrum Karlsruhe / TIB - Technische InformationsbibliothekDEGerman

Superconvergence analysis and error expansion for the Wilson nonconforming finite element

this paper the Wilson nonconforming finite element is considered for solving a class of two-dimensional second-order elliptic boundary value problems. Superconvergence estimates and error expansions are obtained for both uniform and non-uniform rectangular meshes. A new lower bound of the error shows that the usual error estimates are optimal. Finally a discussion on the error behaviour in negative norms shows that there is generally no improvement in the order by going to weaker norms

The hp version of Eulerian-Lagrangian mixed discontinuous finite element methods for advection-diffusion problems

We study the hp version of three families of Eulerian-Lagrangian mixed discontinuous finite element (MDFE) methods for the numerical solution of advection-diffusion problems. These methods are based on a space-time mixed formulation of the advection-diffusion problems. In space, they use discontinuous finite elements, and in time they approximately follow the Lagrangian flow paths (i.e., the hyperbolic part of the problems). Boundary conditions are incorporated in a natural and mass conservative manner. In fact, these methods are locally conservative. The analysis of this paper focuses on advection-diffusion problems in one space dimension. Error estimates are explicitly obtained in the grid size h, the polynomial degree p, and the solution regularity; arbitrary space grids and polynomial degree are allowed. These estimates are asymptotically optimal in both h and p for some of these methods. Numerical results to show convergence rates in h and p of the Eulerian-Lagrangian MDFE methods are presented. They are in a good agreement with the theory