Conditional stability of the Lagrange-Galerkin scheme with numerical quadrature. - Shinya Uchiumi (JSIAM Lett., 2015)

An exactly computable Lagrange-Galerkin scheme for the Navier-Stokes equations and its error estimates. - Masahisa Tabata; Shinya Uchiumi (Math. Comput., 2018)

A Viscosity-Independent Error Estimate of a Pressure-Stabilized Lagrange-Galerkin Scheme for the Oseen Problem. - Shinya Uchiumi (J. Sci. Comput., 2019)

A pressure-stabilized projection Lagrange-Galerkin scheme for the transient Oseen problem. - Shinya Uchiumi (CoRR, 2021)