ERROR ESTIMATES FOR FINITE ELEMENT METHODS APPLIED TO CONTAMINANT TRANSPORT EQUATIONS

[摘要] 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. 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. 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.

[发布机构] Rice University