Absolute p-Refinement of Two-Dimensional Elasticity Problems in the Vicinity of Boundary Solution Singularities
A simple polynomial refinement formulation is developed to study the convergence of the collocation boundary element method for two-dimensional elasticity problems, in the vicinity of a boundary solution singularity. The boundary solution singularity considered here is created by discontinuous boundary conditions prescribed at a point on the boundary. A combination of analytic and numeric integrations are used in evaluating the boundary integrals for discontinuous, constant, and continuous, linear through cubic, solution distributions. The L2 boundary error norm, relative percentage error, and solution norm ratio are used to study convergence of displacements and tractions at the crack tip of a plate fracture problem. The reference for convergence is the solution obtained from a fine mesh of quadratic boundary elements.
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