Multi-layer Perceptron Estimator for the Total Variation Bounded Constant in Limiters for Discontinuous Galerkin Methods

The discontinuous Galerkin (DG) method is widely used in numerical solution of partial differential equations, especially for hyperbolic equations. However, problems containing strong shocks, the DG often needs to be supplemented by a limiter control spurious oscillations and ensure nonlinear stability. total variation bounded (TVB) popular choice can maintain original high order accuracy scheme smooth regions keep sharp non-oscillatory discontinuity transition, when certain TVB constant M chosen adequately. For scalar conservation laws, suitable this based on solid mathematical analysis. systems, there no rigorous guiding principle determination constant, experiments use ad hoc choices experience through trial error. In paper, we develop artificial neural network (ANN) estimator constructing multi-layer perceptron (MLP) model. We generate training data set piecewise functions local maxima, minima, discontinuities. By using supervised learning strategy, MLP model trained offline. proposed gives with robust performance capture shock transitions while maintaining regions. Numerical results new methods one two dimensions are given, its compared classical constant.