6533b828fe1ef96bd1287a6d

RESEARCH PRODUCT

Towards Stable Radial Basis Function Methods for Linear Advection Problems

Philipp ÖFfnerÉLise Le MélédoJan Glaubitz

subject

Work (thermodynamics)AdvectionScalar (physics)Numerical Analysis (math.NA)35L65 41A05 41A30 65D05 65M12Stability (probability)Computational Mathematics10123 Institute of Mathematics510 MathematicsComputational Theory and MathematicsModeling and SimulationPath (graph theory)FOS: MathematicsApplied mathematicsRadial basis functionBoundary value problemMathematics - Numerical Analysis2605 Computational MathematicsEnergy (signal processing)Mathematics2611 Modeling and Simulation1703 Computational Theory and Mathematics

description

In this work, we investigate (energy) stability of global radial basis function (RBF) methods for linear advection problems. Classically, boundary conditions (BC) are enforced strongly in RBF methods. By now it is well-known that this can lead to stability problems, however. Here, we follow a different path and propose two novel RBF approaches which are based on a weak enforcement of BCs. By using the concept of flux reconstruction and simultaneous approximation terms (SATs), respectively, we are able to prove that both new RBF schemes are strongly (energy) stable. Numerical results in one and two spatial dimensions for both scalar equations and systems are presented, supporting our theoretical analysis.

yearjournalcountryeditionlanguage
2021-03-01
10.1016/j.camwa.2021.01.012http://arxiv.org/abs/2101.09623