The addition of fields on different meshes

Let T 1 and T 2 be two (arbitrarily unrelated) meshes of the same domain Ω ⊂ R d , 1 ⩽ d ⩽ 3 . Let V 1 and V 2 be the discrete function spaces induced from these meshes by equipping them with some choice of basis functions. This work discusses the following problem: given two functions f 1 ∈ V f and f 2 ∈ V g , compute f1 + f2. Despite the simple statement of the task, the general solution is not obvious, for the desired sum lies neither in V 1 nor in V 2 , and is not representable on either mesh. The problem is solved by efficiently constructing a supermesh T S of T 1 and T 2 which induces a superspace of both V 1 and V 2 . Once such a mesh is available, the desired quantity may be represented exactly (subject to roundoff).