Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Pointwise best approximation results for Galerkin finite element
  solutions of parabolic problems   In this paper we establish a best approximation property of fully discrete
Galerkin finite element solutions of second order parabolic problems on convex
polygonal and polyhedral domains in the $L^\infty$ norm. The discretization
method uses of continuous Lagrange finite elements in space and discontinuous
Galerkin methods in time of an arbitrary order. The method of proof differs
from the established fully discrete error estimate techniques and for the first
time allows to obtain such results in three space dimensions. It uses elliptic
results, discrete resolvent estimates in weighted norms, and the discrete
maximal parabolic regularity for discontinuous Galerkin methods established by
the authors in [16]. In addition, the proof does not require any relationship
between spatial mesh sizes and time steps. We also establish a local best
approximation property that shows a more local behavior of the error at a given
point.

34
The categories of this paper are: chem-ph
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The categories of this paper are: supr-con
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The categories of this paper are: cond-mat
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The categories of this paper are: atom-ph
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The categories of this paper are: quant-ph
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The categories of this paper are: comp-gas
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The categories of this paper are: bayes-an
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The categories of this paper are: hep-ph
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The categories of this paper are: solv-int
5
The categories of this paper are: gr-qc
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The categories of this paper are: ao-sci
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The categories of this paper are: acc-phys
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The categories of this paper are: plasm-ph
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The categories of this paper are: stat
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The categories of this paper are: nucl-th
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The categories of this paper are: nucl-ex