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arXiv · 2209.05796

A Generalized Weak Galerkin method for Oseen equation

Wenya Qi·Padmanabhan Seshaiyer·Junping Wang
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Abstract

In this work, the authors introduce a generalized weak Galerkin (gWG) finite element method for the time-dependent Oseen equation. The generalized weak Galerkin method is based on a new framework for approximating the gradient operator. Both a semi-discrete and a fully-discrete numerical scheme are developed and analyzed for their convergence, stability, and error estimates. A generalized {\em{inf-sup}} condition is developed to assist the convergence analysis. The backward Euler discretization is employed in the design of the fully-discrete scheme. Error estimates of optimal order are established mathematically, and they are validated numerically with some benchmark examples.

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Wenya Qi, Padmanabhan Seshaiyer, Junping Wang. 2022-09-13. A Generalized Weak Galerkin method for Oseen equation. https://arxiv.org/abs/2209.05796

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