Lee, J. AlexNam, JaewookPasquali, Matteo2015-07-092015-07-092015Lee, J. Alex, Nam, Jaewook and Pasquali, Matteo. "A New Stabilization of Adaptive Step Trapezoid Rule Based on Finite Difference Interrupts." <i>SIAM Journal on Scientific Computing,</i> 37, no. 2 (2015) Society for Industrial and Applied Mathematics: A725-A746. http://dx.doi.org/10.1137/140966915.https://hdl.handle.net/1911/80853The adaptive step trapezoid rule (TR) is a generally effective numerical integrator, but it is prone to ringing instability and solution stall. We introduce a new stabilization algorithm based on finite difference interrupts (FDI) that reduces ringing and prevents stall. Unlike previously reported stabilization schemes, our algorithm achieves stability and second order accuracy without incurring significant computational cost or spurious diffusion. TR with FDI is at least as stable and accurate as existing methods when solving the prototypical scalar problem. We demonstrate that it has better stability, accuracy, and cost when solving the tightly coupled system describing free surface flows of viscoelastic liquids. Though we demonstrate TR with FDI in the context of a finite element method-of-lines, it is applicable to any TR-based algorithm.engArticle is made available in accordance with the publisher's policy and may be subject to US copyright law. Please refer to the publisher's site for terms of use.Journal articletrapezoid ruleAdams -- Bashforth -- Moultonmethod-of-linesadaptive time stepfluid mechanicsfinite element methodringing instabilitystiff PDEhttp://dx.doi.org/10.1137/140966915