Conditional stability of the Lagrange-Galerkin scheme with numerical quadrature

抄録

We show conditional stability of the Lagrange-Galerkin scheme with numerical quadrature for the convection-diffusion equation. We consider the scheme under the assumption that quadrature points are inside the element and that the time increments are sufficiently small. Our analysis covers general triangular or tetrahedral meshes and arbitrary smooth velocities. We present some numerical examples that reflect the theoretical result.