We present the high-order lightning Virtual Element Method. The lightning VEM is a new virtual element scheme that does not require any stabilization. Rational functions are used to approximate the virtual basis functions, hence avoiding the need for stabilization and bypassing the need of projecction operators. In this paper, we describe how to obtain the approximate basis functions and how to construct the virtual element space for various values of degree k. In the last section, we show numerical results validating the proposed method.

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The High-Order Lightning Virtual Element Method

  • Manuel Trezzi,
  • Umberto Zerbinati

摘要

We present the high-order lightning Virtual Element Method. The lightning VEM is a new virtual element scheme that does not require any stabilization. Rational functions are used to approximate the virtual basis functions, hence avoiding the need for stabilization and bypassing the need of projecction operators. In this paper, we describe how to obtain the approximate basis functions and how to construct the virtual element space for various values of degree k. In the last section, we show numerical results validating the proposed method.