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Mathematics of Computation

Published by the American Mathematical Society since 1960 (published as Mathematical Tables and other Aids to Computation 1943-1959), Mathematics of Computation is devoted to research articles of the highest quality in computational mathematics.

ISSN 1088-6842 (online) ISSN 0025-5718 (print)

The 2020 MCQ for Mathematics of Computation is 1.78.

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Analysis of the finite element variational crimes in the numerical approximation of transonic flow
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by Harald Berger and Miloslav Feistauer PDF
Math. Comp. 61 (1993), 493-521 Request permission

Abstract:

The paper presents a detailed theory of the finite element approximations of two-dimensional transonic potential flow. We consider the boundary value problem for the full potential equation in a general bounded domain $\Omega$ with mixed Dirichlet-Neumann boundary conditions. In the discretization of the problem we proceed as usual in practice: the domain $\Omega$ is approximated by a polygonal domain, conforming piecewise linear triangular elements are used, and the integrals are evaluated by numerical quadratures. Using a new version of entropy compactification of transonic flow and the theory of finite element variational crimes for nonlinear elliptic problems, we prove the convergence of approximate solutions to the exact physical solution of the continuous problem, provided its existence can be shown.
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Additional Information
  • © Copyright 1993 American Mathematical Society
  • Journal: Math. Comp. 61 (1993), 493-521
  • MSC: Primary 65N30; Secondary 65N12, 76H05, 76M10
  • DOI: https://doi.org/10.1090/S0025-5718-1993-1192967-6
  • MathSciNet review: 1192967