A mass-lumped mixed finite element method for acoustic wave propagation

A mass-lumped mixed finite element method for Maxwell's equations

“…This ensures that the method ( 5)-( 6) also has good approximation properties. By a slight adoption of the results given in [5], we obtain Lemma 2. Let E, H be a smooth solution of ( 1)-( 2) and let E h (0) and H h (0) be chosen appropriately.…”

“…The properties (i)-(ii) follow directly form the construction. From the particular choice of basis functions, one can deduce that M µ is diagonal and M ε is block-diagonal; see [5,11] for details. This implies conditions (iii).…”

“…For structured meshes and isotropic coefficients, one can observe second order convergence also for line integrals of the electric field along edges of the mesh. In addition, second convergence can also obtained for unstructured meshes by a non-local post-processing strategy; see [5] for details.…”

Comparison of the hybrid and multipoint‐flux method

“…The mass lumped variant does not require these additional computations. For the first order method, we conducted an analysis for the acoustic wave propagation in [1]. In future work, we will discuss second order elements, as well as further applications to Maxwell's equations.…”

A second order multipoint flux mixed finite element method on hybrid meshes

“…Related mass lumping strategies have been developed for rectangular and simplicial elements in [13] and in [16,17] for Maxwell's equations; let us refer to [12] for an overview. In [14], we provided a full convergence analysis for a mixed finite element approximation of the acoustic wave equation with mass lumping based on the method of Wheeler and Yotov [28].…”