  We explain four variants of an adaptive finite element method with cubic
splines and compare their performance in simple elliptic model problems. The
methods in comparison are Truncated Hierarchical B-splines with two different
refinement strategies, T-splines with the refinement strategy introduced by
Scott et al. in 2012, and T-splines with an alternative refinement strategy
introduced by some of the authors. In four examples, including singular and
non-singular problems of linear elasticity and the Poisson problem, the
H1-errors of the discrete solutions, the number of degrees of freedom as well
as sparsity patterns and condition numbers of the discretized problem are
compared.
