Solutions to harmonic and biharmonic problems with discontinuous boundary conditions by collocation methods using multiquadrics as basis functions

Abstract

Behaviors of the global and local collocation methods that use multiquadrics as basis functions in solving problems having continuous boundary conditions are well known. In this paper, harmonic and biharmonic problems having discontinuous boundary conditions are solved by these methods. Solutions to two test problems are investigated. The first test problem is a heat conduction problem with discontinuous temperature at the boundary. The second test problem is the Stokes flow problem in a lid-driven square cavity. Results show that performances the global and local collocation methods depend on the shape parameter of multiquadrics, and solutions by the global collocation method are more sensitive to the shape parameter than the local collocation method.