A theoretical study of COmpRessed SolvING for advection-diffusion-reaction problems

A theoretical study of COmpRessed SolvING for advection-diffusion-reaction problems

We present a theoretical analysis of the CORSING (COmpRessed SolvING) method for the numerical approximation of partial differential equations based on compressed sensing. In particular, we show that the best s-term approximation of the weak solution of a PDE with respect to an orthonormal system of N trial functions, can be recovered via a Petrov-Galerkin approach using m N orthonormal test fu...

Robust a-posteriori estimator for advection-diffusion-reaction problems

We propose an almost-robust residual-based a-posteriori estimator for the advection-diffusion-reaction model problem. The theory is developed in the one-dimensional setting. The numerical error is measured with respect to a norm which was introduced by the author in 2005 and somehow plays the role that the energy norm has with respect to symmetric and coercive differential operators. In particu...

Discontinuous Galerkin Methods for Advection-diffusion-reaction Problems

We apply the weighted-residual approach recently introduced in [7] to derive dis-continuous Galerkin formulations for advection-diffusion-reaction problems. We devise the basic ingredients to ensure stability and optimal error estimates in suitable norms, and propose two new methods. 1. Introduction. In recent years Discontinuous Galerkin methods have become increasingly popular, and they have ...

Hierarchical Model (himod) Reduction for Advection-diffusion-reaction Problems

The effective numerical description of challenging problems arising from engineering applications demands often the selection of an appropriate reduced aka ”surrogate” model. The latter should result from a trade-off between reliability and computational affordability (see, e.g., [1, 8]). Different approaches can be pursued to set up the reduced model. In some cases, one can take advantage of s...

Discontinuous Galerkin Methods for Advection-Diffusion-Reaction Problems