An efficient finite difference method for the shallow water equations. - Lukas Lundgren; Ken Mattsson (J. Comput. Phys., 2020)

A residual-based artificial viscosity finite difference method for scalar conservation laws. - Vidar Stiernström; Lukas Lundgren; Murtazo Nazarov; Ken Mattsson (J. Comput. Phys., 2021)

A high-order artificial compressibility method based on Taylor series time-stepping for variable density flow. - Lukas Lundgren; Murtazo Nazarov (J. Comput. Appl. Math., 2023)

A fully conservative and shift-invariant formulation for Galerkin discretizations of incompressible variable density flow. - Lukas Lundgren; Murtazo Nazarov (J. Comput. Phys., 2024)

Viscous Regularization of the MHD Equations. - Tuan Anh Dao; Lukas Lundgren; Murtazo Nazarov (SIAM J. Appl. Math., 2024)

A high-order residual-based viscosity finite element method for incompressible variable density flow. - Lukas Lundgren; Murtazo Nazarov (J. Comput. Phys., 2024)

A potential energy conserving finite element method for turbulent variable density flow: Application to glacier-fjord circulation. - Lukas Lundgren; Christian Helanow; Jonathan Wiskandt; Inga Monika Koszalka; Josefin Ahlkrona (J. Comput. Phys., 2025)

Stability analysis of the free-surface Stokes problem and an unconditionally stable explicit scheme. - Igor Tominec; Lukas Lundgren; André Löfgren; Josefin Ahlkrona (CoRR, 2025)