2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/182473We study a space-time finite element approach for the nonhomogeneous wave equation using a continuous time Galerkin method. We present fully implicit examples in 1+1, 2+1, and 3+1 dimensions using linear quadrilateral, hexahedral, and tesseractic elements. Krylov solvers with additive Schwarz preconditioning are used for solving the linear system. We introduce a time decomposition strategy in preconditioning which significantly improves performance when compared with unpreconditioned cases.9 pages, 5 figures, 5 tablesGeneral Relativity and Quantum Cosmologytext