A space-time hp-interpolation-based certified reduced basis method for Burgers' equation

We present a space-time interpolation-based certified reduced basis method for Burgers' equation over the spatial interval (0, 1) and the temporal interval (0, T] parametrized with respect to the Peclet number. We first introduce a Petrov–Galerkin space-time finite element discretization which enjoys a favorable inf–sup constant that decreases slowly with Peclet number and final time T. We then consider an hp interpolation-based space-time reduced basis approximation and associated Brezzi–Rappaz–Raviart a posteriori error bounds. We describe computational offline–online decomposition procedures for the three key ingredients of the error bounds: the dual norm of the residual, a lower bound for the inf–sup constant, and the space-time Sobolev embedding constant. Numerical results demonstrate that our space-time formulation provides improved stability constants compared to classical L2-error estimates; the error bounds remain sharp over a wide range of Peclet numbers and long integration times T, in marked contrast to the exponentially growing estimate of the classical formulation for high Peclet number cases.

• Publication year

  2014

• Venue

  Mathematical Models and Methods in Applied Sciences

• Publication date

  2014-05-20

• Fields of study

  Mathematics, Physics

• Identifiers
  DOI 10.1142/S0218202514500110
• External record

  Open on Semantic Scholar

• Source metadata

  Semantic Scholar

• No claims are published for this paper.

• No concepts are published for this paper.

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