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pfDErO

Figure B.14 Computational domain of the cone-sphere problem.

pfDErO

Figure B.14 Computational domain of the cone-sphere problem.

Figure B.16 Details of the singularity of \Ei,.lt\ 50,000).

Figure B.17 The /ip-mesh, global view. Large seventh-order elements are used far from the singularity and small quadratic elements at the tip of the cone.

Figure B.18 The ftp-mesh, details of the tip of the cone (zoom = 50,000).

The geometry of the piecewise-affine mesh was identical to the hp-mesh, but the piecewise-affine mesh was moreover uniformly subdivided in order to reach the required level of accuracy (each edge was split into 48 equally long parts). An efficiency comparison is shown in Table B.3.

Table B.3 Comparison of the number of DOF, relative error in the if1 -norm, number of iterations of the matrix solver, and the CPU-time.

Affine elements hp elements

DOF 488542 3317

Error 0.5858% 0.2804% Iterations 859 44

CPU time 30 min 10.53 sec

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