English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Tools annual

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Tools monthly

Global: Zendy Plus monthly

Presents the access of premium content as premium feature

Premium Content

Global: Zendy Plus annual

Global: Zendy Free Plan

We consider the one-dimensional shallow water equations (SW) in a finitechannel with variable bottom topography. We pose several initial-boundary-valueproblems for the SW system, including problems with transparent(characteristic) boundary conditions in the supercritical and the subcriticalcase. We discretize these problems in the spatial variable by standardGalerkin-finite element methods and prove L^2-error estimates for the resultingsemidiscrete approximations. We couple the schemes with the 4th order-accurate,explicit, classical Runge-Kutta time stepping procedure and use the resultingfully discrete methods in numerical experiments of shallow water wavepropagation over variable bottom topographies with several kinds of boundaryconditions. We discuss issues related to the attainment of a steady state ofthe simulated flows, including the good balance of the schemes.

Galerkin finite element methods for the Shallow Water equations over variable bottom