A One-Dimensional Finite-Element Model for Two-Dimensional Glacier Flow

Abstract A description of the reduction of two-dimensional equilibrium equations to one-dimensional form via the Kantorovich method is given. An appropriate interpolation function is obtained by relating basal shear stress to sliding velocity and integrating the constitutive model through the depth of ice. An example is presented which demonstrates the ability of the numerical model to effect solutions which are in good agreement with those obtained via full two-dimensional finite-element models; however, at a small fraction of computational and data input efforts. The technique described for the reduction of the equilibrium equations can also be used to convert three-dimensional stress equilibrium to two-dimensional form.