An HR-method of mesh refinement for boundary element method

This paper describes a mesh reÞnement technique for boundary element method in which the number of elements, the size of elements and the element end location are determined iteratively in order to obtain a user speciÞed accuracy. The method uses ¸ 1 norm as a measure of error in the density function and a grading function that ensures that error over each element is the same. The use of grading function along with ¸ 1 norm makes the mesh reÞnement technique applicable to Direct and Indirect boundary element method formulation for a variety of boundary element method applications. Numerical problems in elastostatics, fracture mechanics, and bending of plate solved using Direct and Indirect method in which the density functions are approximated by Linear Lagrange, Quadratic Lagrange or Cubic Hermite polynomials validate the e¤ectiveness of the proposed mesh reÞnement technique