Generalized Time Integration Schemes for Space-Time Moving Finite\n Elements

2013/10/28 by Randolph E. Bank, Bank, Randolph E., Maximilian S. Metti +1
Engineering · Mathematics · #Advanced Numerical Methods in Computational Mathematics #Electromagnetic Simulation and Numerical Methods #FOS: Mathematics #Numerical Analysis (math.NA) #Numerical methods for differential equations

paper · pdf · doi:10.48550/arxiv.1310.7611

openalex publication_date 2013/10/28 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper, we analyze and provide numerical illustrations for a moving\nfinite element method applied to convection-dominated, time-dependent partial\ndifferential equations. We follow a method of lines approach and utilize an\nunderlying tensor-product finite element space that permits the mesh to evolve\ncontinuously in time and undergo discontinuous reconfigurations at discrete\ntime steps. We employ the TR-BDF2 method as the time integrator for piecewise\nquadratic tensor-product spaces, and provide an almost symmetric error estimate\nfor the procedure. Our numerical results validate the efficacy of these moving\nfinite elements.\n

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