A convergence analysis to the weak solution is derived for interior penalty discontinuous Galerkin methods applied to the heat equation in two and three dimensions under general mixed boundary conditions. Strong convergence is established in the DG norm, as well as in the L norm, in space and in the L norm in time.

Article history: Received 12 September 2013 Received in revised form 8 April 2014 Accepted 3 July 2014 Available online 15 July 2014

Article history: Received 21 February 2012 Received in revised form 30 May 2012 Accepted 4 June 2012 Available online 16 June 2012

Article history: Received 27 March 2011 Accepted 3 May 2012 Available online 15 May 2012

numerical solutions obtained by the meshless local petrov–galerkin (mlpg) method are presented for two-dimensional steady-state heat conduction problems. the mlpg method is a truly meshless approach, and neither the nodal connectivity nor the background mesh is required for solving the initial-boundary-value problem. the penalty method is adopted to efficiently enforce the essential boundary co...