Title: Reduced continuity finite element methods for first order
scalar hyperbolic equationsQuadrilateral H(div) finite elements.
Authors: Da_mu Cai and Richard S. Falk
Source: RAIRO. M2AN vol. 28, no 6 (1994), pp. 667-698
Status: Published
Abstract: Two explicit fimte element methods for a first order linear
hyperbolic problem in R^2 are proposed and analyzed. These schemes are
designed to produce an approximate solution which has a certain number of
continuous moments across element edges. L^2 error estimates of order O (n +
1/2 )for both schemes are obtained. This is the same convergence rate known
for tne discontinuons Galerkin method, but is achieved with fewer
computations. Some numerical results for these methods are presented and
comparisons are made with other exphcit finite element methods for this
problem previously studied in the literature.