Illustrative problems P1 and P2. The following two problems demonstrate the finite element method. P1 is a one-dimensional problem : {″ = (,), = =, where is given, is an unknown function of , and ″ is the second derivative of with respect to .. P2 is a two-dimensional problem (Dirichlet problem) : {(,) + (,) = (,), =, where is a connected open region in the (,) plane whose boundary is …

Definition and terminology. Formally, a set S is called finite if there exists a bijection: {, …,} for some natural number n.The number n is the set's cardinality, denoted as |S|.The empty set { } or ∅ is considered finite, with cardinality zero.. If a set is finite, its elements may be written — in many ways — in a sequence: ,, …, (, ). In combinatorics, a finite set with n elements ...