Low-order finite elements for parameter identification in groundwater flow

New Second-Order Finite Difference Scheme for the Problem of Contaminant in Groundwater Flow

We develop a new efficient second-order finite difference scheme for two-dimensional problem of contaminant in groundwater flow. Theoretical analysis shows that the scheme is second-order convergence in the L2 norm and is unconditionally stable. Numerical results demonstrate that the error measures of the second-order scheme are several times smaller than those of the standard implicit finite d...

Algebraic multigrid for higher-order finite elements

Two related approaches for solving linear systems that arise from a higher-order finite element discretization of elliptic partial differential equations are described. The first approach explores direct application of an algebraic-based multigrid method (AMG) to iteratively solve the linear systems that result from higher-order discretizations. While the choice of basis used on the discretizat...

Algebraic Multigrid for Moderate Order Finite Elements

The paper discusses algebraic multigrid (AMG) methods for the solution of large sparse linear systems arising from the discretization of scalar elliptic partial differential equations with Lagrangian finite elements of order at most 4. The resulting system matrices do not have the M-matrix property that is used by standard analyzes of classical AMG and aggregation-based AMG methods. A unified a...

Parameter Estimation in Groundwater Flow Models with Distributedand Pointwise Observations

We present in this paper some results concerning the least sqaures estimation of parameters in a groundwater ow model. As is typically the case in eld studies, the form of the data is pointwise observation of hydraulic head and hydraulic conductivity at a discrete collection of observation well sites. We prove continuous dependence results for the solution of the groundwater ow equation, with r...

The Finite Layer Method for Groundwater Flow Models