Stefano Berrone, Andrea Borio, Davide Fassino, Francesca Marcon
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Abstract
In this work, we present and analyze a Stabilization-free Virtual Element high order scheme for 2D second order elliptic equation. This method is characterized by the definition of new polynomial projections that allow the definition of structure-preserving schemes. We provide a necessary and sufficient condition on the polynomial projection space that ensure the well-posedness of the scheme and we derive optimal a priori error estimates. Several numerical tests assess the stability of the method and the robustness in solving problems characterized by anisotropies.
期刊介绍：
Computer Methods in Applied Mechanics and Engineering stands as a cornerstone in the realm of computational science and engineering. With a history spanning over five decades, the journal has been a key platform for disseminating papers on advanced mathematical modeling and numerical solutions. Interdisciplinary in nature, these contributions encompass mechanics, mathematics, computer science, and various scientific disciplines. The journal welcomes a broad range of computational methods addressing the simulation, analysis, and design of complex physical problems, making it a vital resource for researchers in the field.
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