54 research outputs found
Weak convergence of finite element approximations of linear stochastic evolution equations with additive noise II. Fully discrete schemes
We present an abstract framework for analyzing the weak error of fully
discrete approximation schemes for linear evolution equations driven by
additive Gaussian noise. First, an abstract representation formula is derived
for sufficiently smooth test functions. The formula is then applied to the wave
equation, where the spatial approximation is done via the standard continuous
finite element method and the time discretization via an I-stable rational
approximation to the exponential function. It is found that the rate of weak
convergence is twice that of strong convergence. Furthermore, in contrast to
the parabolic case, higher order schemes in time, such as the Crank-Nicolson
scheme, are worthwhile to use if the solution is not very regular. Finally we
apply the theory to parabolic equations and detail a weak error estimate for
the linearized Cahn-Hilliard-Cook equation as well as comment on the stochastic
heat equation
Error estimates for the discretization of the velocity tracking problem
In this paper we are continuing our work (Casas and Chrysafinos, SIAM J Numer Anal 50(5):2281â2306, 2012), concerning a priori error estimates for the velocity tracking of two-dimensional evolutionary NavierâStokes flows. The controls are of distributed type, and subject to point-wise control constraints. The discretization scheme of the state and adjoint equations is based on a discontinuous time-stepping scheme (in time) combined with conforming finite elements (in space) for the velocity and pressure. Provided that the time and space discretization parameters, t and h respectively, satisfy t = Ch2, error estimates of order O(h2) and O(h 3/2 â 2/p ) with p > 3 depending on the regularity of the target and the initial velocity, are proved for the difference between the locally optimal controls and their discrete approximations, when the controls are discretized by the variational discretization approach and by using piecewise-linear functions in space respectively. Both results are based on new duality arguments for the evolutionary NavierâStokes equations
Factors influencing stream baseflow transit times in tropical montane watersheds
Stream water mean transit time (MTT) is a fundamental hydrologic parameter
that integrates the distribution of sources, flow paths, and storages present
in catchments. However, in the tropics little MTT work has been carried out,
despite its usefulness for providing important information on watershed
functioning at different spatial scales in (largely) ungauged basins. In
particular, very few studies have quantified stream MTTs or have related these
to catchment characteristics in tropical montane regions. Here we examined
topographic, land use/cover and soil hydraulic controls on baseflow transit
times for nested catchments (0.1â34âŻkm2) within a humid mountainous
region, underlain by volcanic soil (Andisols) in central Veracruz (eastern
Mexico). We used a 2-year record of bi-weekly isotopic composition of
precipitation and stream baseflow data to estimate MTT. Land use/cover and
topographic parameters (catchment area and form, drainage density, slope
gradient and length) were derived from geographic information system (GIS) analysis. Soil water retention
characteristics, and depth and permeability of the soilâbedrock interface
were obtained from intensive field measurements and laboratory analysis.
Results showed that baseflow MTTs ranged between 1.2Â and 2.7Â years across the
12Â study catchments. Overall, MTTs across scales were mainly controlled by
catchment slope and the permeability observed at the soilâbedrock interface.
In association with topography, catchment form and the depth to the
soilâbedrock interface were also identified as important features
influencing baseflow MTTs. The greatest differences in MTTs were found both
within groups of small (0.1â1.5âŻkm2) and large (14â34âŻkm2)
catchments. Interestingly, the longest stream MTTs were found in the headwater
cloud forest catchments
Runoff generation in a steep, tropical montane cloud forest catchment on permeable volcanic substrate
Investigation into Material Strength and Direction of Applied Forces to Assess Bonding Behaviour of Micro-concrete
Ecohydrological advances and applications in plant-water relations research: a review
Aims
The field of ecohydrology is providing new theoretical frameworks
and methodological approaches for understanding the complex
interactions and feedbacks between vegetation and hydrologic
flows at multiple scales. Here we review some of the major scientific
and technological advances in ecohydrology as related to understanding
the mechanisms by which plantâwater relations influence
water fluxes at ecosystem, watershed and landscape scales.
Important Findings
We identify several cross-cutting themes related to the role of plantâ
water relations in the ecohydrological literature, including the contrasting
dynamics of water-limited and water-abundant ecosystems,
transferring information about water fluxes across scales, understanding
spatiotemporal heterogeneity and complexity, ecohydrological
triggers associated with threshold behavior and shifts
between alternative stable states and the need for long-term data sets
at multiple scales. We then show how these themes are embedded
within three key research areas where improved understanding of
the linkages between plantâwater relations and the hydrologic cycle
have led to important advances in the field of ecohydrology: upscaling
water fluxes from the leaf to the watershed and landscape, effects
of plantâsoil interactions on soil moisture dynamics and controls
exerted by plant water use patterns and mechanisms on streamflow
regime. In particular, we highlight several pressing environmental
challenges facing society today where ecohydrology can contribute
to the scientific knowledge for developing sound management and
policy solutions.We conclude by identifying key challenges and opportunities
for advancing contributions of plantâwater relations research
to ecohydrology in the future
Present distribution of the genus Elodea in the Alsatian Upper Rhine floodplain (France) with a special focus on the expansion of Elodea nuttallii St. John during recent decades
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