A priori error estimates for sobolev equation using HDG method

Abstract

A hybridizable discontinuous Galerkin (HDG) method is introduced and analyzed to solve the Sobolev equation. The analysis includes the derivation of a priori error estimates, demonstrating that the approximations for both the flux and displacement exhibit convergence at a rate of order where h represents the mesh size and k is the polynomial degree. Additionally, the solution is further improved by applying a post-processing technique, and it has been demonstrated that, for , the post-processed solution converges at an enhanced rate of order . A fully discrete scheme is also proposed, achieving second-order accuracy in time; numerical results are needed to validate the theoretical results.