A Solution of the Heat Equation with the Discontinuous Galerkin Method Using a Multilivel Calculation Method That Utilizes a Multiresolution Wavelet Basis
Robert Gregory Brown · ODU Digital Commons (Old Dominion University) · 2019
A numerical method to solve the parabolic problem is developed that utilizes the Discontinuous Galerkin Method for space and time discretization. A multilevel method is employed in the space variable. It is shown that use of this process yields the same level of accuracy as the standard Discontinuous Galerkin Method for the heat equation, but with cheaper computational cost. The results are demonstrated using a standard one-dimensional homogeneous heat problem.