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Boundary value problems (BVPs) with partial differential equations are often models for processes in nature and engineering. A crucial requirement to become a useful and accepted model is that the solution of the BVP possesses important physical properties of the modeled process, like to take only physically admissible values. In practice, the solution of a BVP can be generally only approximated by numerical simulations. Thus, in order that a numerical solution is meaningful and accepted by practitioners, it is of utmost importance that physically relevant properties of the solution of the BVP are also present in the numerical solution.

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Introduction

  • 章节

  • 发表日期：

    2025年

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  • Gabriel R. Barrenechea,
  • Volker John,
  • Petr Knobloch

摘要

Boundary value problems (BVPs) with partial differential equations are often models for processes in nature and engineering. A crucial requirement to become a useful and accepted model is that the solution of the BVP possesses important physical properties of the modeled process, like to take only physically admissible values. In practice, the solution of a BVP can be generally only approximated by numerical simulations. Thus, in order that a numerical solution is meaningful and accepted by practitioners, it is of utmost importance that physically relevant properties of the solution of the BVP are also present in the numerical solution.