Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: An Adaptive Stable Space-Time FE Method for the Shallow Water Equations   We consider the finite element (FE) approximation of the shallow water
equations (SWE) by considering discretizations in which both space and time are
established using an unconditionally stable FE method. Particularly, we
consider the automatic variationally stable FE (AVS-FE) method, a type of
discontinuous Petrov-Galerkin (DPG) method. The philosophy of the DPG method
allows us to break the test space and achieve unconditionally stable FE
approximations as well as accurate a posteriori error estimators upon solution
of a saddle point system of equations. The resulting error indicators allow us
to employ mesh adaptive strategies and perform space-time mesh refinements,
i.e., local time stepping.
  We derive a priori error estimates for the AVS-FE method and linearized SWE
and perform numerical verifications to confirm corresponding asymptotic
convergence behavior. In an effort to keep the computational cost low, we
consider an alternative space-time approach in which the space-time domain is
partitioned into finite sized space-time slices. Hence, we can perform
adaptivity on each individual slice to preset error tolerances as needed for a
particular application. Numerical verifications comparing the two alternatives
indicate the space-time slices are superior for simulations over long times,
whereas the solutions are indistinguishable for short times. Multiple numerical
verifications show the adaptive mesh refinement capabilities of the AVS-FE
method, as well the application of the method to commonly applied benchmarks
for the SWE.

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The categories of this paper are: q-alg
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The categories of this paper are: solv-int
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The categories of this paper are: supr-con
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The categories of this paper are: econ
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The categories of this paper are: stat
4
The categories of this paper are: cond-mat
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The categories of this paper are: ao-sci
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The categories of this paper are: comp-gas
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The categories of this paper are: chem-ph
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The categories of this paper are: alg-geom
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The categories of this paper are: plasm-ph
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The categories of this paper are: dg-ga
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The categories of this paper are: gr-qc
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The categories of this paper are: q-bio
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The categories of this paper are: funct-an
0
The categories of this paper are: hep-ph