2017/05/13 by Stephen E. Moore, Moore, Stephen Edward · 2 citations
Engineering · Mathematics · #65N12 #65N15 #65N30 #Advanced Numerical Analysis Techniques #FOS: Mathematics #Iterative Methods for Nonlinear Equations #Numerical Analysis (math.NA)
paper · pdf · doi:10.48550/arxiv.1705.04829
openalex publication_date 2017/05/13 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We present and analyze a stable space-time multi-patch discontinuous Galerkin\nIsogeometric Analysis (dG-IgA) scheme for the numerical solution of parabolic\nevolution equations in moving space-time computational domains. Following\n citeLangerMooreNeumueller:2016a, we use a time-upwind test function and\napply multi-patch discontinuous Galerkin IgA methodology for discretizing the\nevolution problem both in space and in time. This yields a discrete bilinear\nform which is elliptic on the IgA space with respect to a space-time dG norm.\nThis property together with a corresponding boundedness property, consistency\nand approximation results for the IgA spaces yields an \a priori\ndiscretization error estimate with respect to the space-time dG norm. The\ntheoretical results are confirmed by several numerical experiments with low-\nand high-order IgA spaces.\n