| L('2)(L('2)) error estimates for a continuous time Galerkin approximation to the solution of a system of nonlinear parabolic equations, which model contaminant transport in groundwater, are derived using standard energy norm methods. Dirichlet and Neumann type boundary conditions are treated.;By comparing a nonlinear parabolic Galerkin approximation to a linear parabolic Galerkin projection, L('2)(H('1)) error estimates for the nonlinear Galerkin approximation and L('2)(L('2)) error estimates for the time derivative of the approximation are derived. A parabolic duality argument is then employed to derive optimal L('2)(L('2)) error estimates for the nonlinear parabolic equation.;First, L('2)(H('1)) error estimates for a linear Galerkin projection and L('2)(L('2)) error estimates for the time derivative of the linear Galerkin projection are obtained. With these estimates, a parabolic duality argument gives an optimal L('2)(L('2)) error estimate for the linear parabolic projection. |
