Sergio Gomez, Lorenzo Mascotto, Andrea Moiola, Ilaria Perugia
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SIAM Journal on Numerical Analysis, Volume 62, Issue 1, Page 199-228, February 2024. Abstract. We propose and analyze a space-time virtual element method for the discretization of the heat equation in a space-time cylinder, based on a standard Petrov–Galerkin formulation. Local discrete functions are solutions to a heat equation problem with polynomial data. Global virtual element spaces are nonconforming in space, so that the analysis and the design of the method are independent of the spatial dimension. The information between time slabs is transmitted by means of upwind terms involving polynomial projections of the discrete functions. We prove well posedness and optimal error estimates for the scheme, and validate them with several numerical tests.
期刊介绍：
SIAM Journal on Numerical Analysis (SINUM) contains research articles on the development and analysis of numerical methods. Topics include the rigorous study of convergence of algorithms, their accuracy, their stability, and their computational complexity. Also included are results in mathematical analysis that contribute to algorithm analysis, and computational results that demonstrate algorithm behavior and applicability.
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