An adaptive viscosity regularization approach for the numerical solution of conservation laws: Application to finite element methods

• Published in: Journal of computational physics Vol. 494; no. C; p. 112507
• Main Authors: Nguyen, Ngoc Cuong, Vila-Pérez, Jordi, Peraire, Jaime
• Format: Journal Article
• Language: English
• Published: United States Elsevier Inc 01.12.2023; Elsevier
• Subjects: Adaptive viscosity; Conservation laws; Discontinuous Galerkin methods; Finite element methods; Shock capturing; Shock waves; Conservation laws; Adaptive viscosity; Shock waves; Discontinuous Galerkin methods; Finite element methods; Shock capturing

We introduce an adaptive viscosity regularization approach for the numerical solution of systems of nonlinear conservation laws with shock waves. The approach seeks to solve a sequence of regularized problems consisting of the system of conservation laws and an additional Helmholtz equation for the...