ERROR ESTIMATES FOR FINITE ELEMENT METHODS APPLIED TO CONTAMINANT TRANSPORT EQUATIONS

• Main Author: PALMER, OWEN JAMES
• Format: Others
• Language: English
• Published: 2007
• Subjects: Mathematics
• Online Access: http://hdl.handle.net/1911/15777

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.