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Some Applications of the PDE Solver FDEM with Error Estimate

In: High Performance Computing in Science and Engineering, Garching/Munich 2007

Author

Listed:
  • Torsten Adolph

    (Institute for Scientific Computing, Forschungszentrum Karlsruhe)

  • Willi Schönauer

    (Institute for Scientific Computing, Forschungszentrum Karlsruhe)

Abstract

We give a brief overview of the Finite Difference Element Method (FDEM), above all how an explicit estimate of the error is obtained. Then for some academic examples, the estimated and exact error are compared showing the quality of the estimate. The nonlinear PDE for the numerical simulation of the temperature in a high pressure Diesel injection pump, where the domain consists of three subdomains, is solved. Then the temperature in a power semiconductor module with six power chips is numerically simulated. This is a time-dependent problem in 3-D, where the solution domain consists of two subdomains. The third problem is the numerical simulation of a microreactor. For all these problems, the global error estimate shows the quality of the solution, and it would be very difficult to obtain a quality control of the solution by conventional grid refinement tests.

Suggested Citation

  • Torsten Adolph & Willi Schönauer, 2009. "Some Applications of the PDE Solver FDEM with Error Estimate," Springer Books, in: Siegfried Wagner & Matthias Steinmetz & Arndt Bode & Matthias Brehm (ed.), High Performance Computing in Science and Engineering, Garching/Munich 2007, pages 443-457, Springer.
    • Handle: RePEc:spr:sprchp:978-3-540-69182-2_36
    DOI: 10.1007/978-3-540-69182-2_36
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