Space-time finite element analysis of the advection-diffusion equation using Galerkin/least-square stabilization
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2023-07-03
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arXiv
Abstract
We present a full space-time numerical solution of the advection-diffusion equation using a continuous Galerkin finite element method. The Galerkin/least-square method is employed to ensure stability of the discrete variational problem. In the full space-time formulation, time is considered another dimension, and the time derivative is interpreted as an additional advection term of the field variable. We derive a priori error estimates and illustrate spatio-temporal convergence with several numerical examples. We also derive a posteriori error estimates, which coupled with adaptive space-time mesh refinement provide efficient and accurate solutions. The accuracy of the space-time solutions is illustrated against analytical solutions as well as against numerical solutions using a conventional time-marching algorithm.
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This is a preprint from Khara, Biswajit, Kumar Saurabh, Robert Dyja, Anupam Sharma, and Baskar Ganapathysubramanian. "Space-time finite element analysis of the advection-diffusion equation using Galerkin/least-square stabilization." arXiv preprint arXiv:2307.00822 (2023). doi: https://doi.org/10.48550/arXiv.2307.00822. Copyright The Authors 2023. CC By