Mathematics of Computation
Galerkin methods, Error analysis (Mathematics), Numerical analysis, Mathematical statistics, Elliptic functions
We introduce a new technique for the error analysis of hybridizable discontinuous Galerkin (HDG) methods. The technique relies on the use of a new projection whose design is inspired by the form of the numerical traces of the methods. This renders the analysis of the projections of the discretization errors simple and concise. By showing that these projections of the errors are bounded in terms of the distance between the solution and its projection, our studies of influence of the stabilization parameter are reduced to local analyses of approximation by the projection. We illustrate the technique on a specific HDG method applied to a model second-order elliptic problem.
A Projection-Based Error Analysis of HDG Methods (2010). Mathematics of Computation, 79(271), 1351-1367.