The h, p and h-p versions of the finite element method in 1 dimension. II. The error analysis of the h- and h-p versions
This paper concentrates on h and h-p versions of FEM. Generally, the h- version of FEM has the degree of elements fixed and the convergence is achieved by the refinement of the mesh. The h-p version combines both approaches, the p-version and h-version. The same model problem as in Part I [ibid. 49, 577-612 (1986; reviewed above)] is considered. The paper is mainly concerned with the relation between the relative error in the energy norm and the number of degrees of freedom. The authors show that the selection of the mesh and degree of elements is essential for the performance of the method. More exactly, the proper selection of the h-p version leads to the exponential rate of convergence while the h-version with improper mesh, gives very low algebraic rate when a singularity is present.
scientific article; zbMATH DE number 3994957