# American Institute of Mathematical Sciences

September  2007, 6(3): 719-740. doi: 10.3934/cpaa.2007.6.719

## Error analysis of the p-version discontinuous Galerkin method for heat transfer in built-up structures

 1 Thermal Structures Branch, Structure Division, NASA Langley Research Center, Hampton, VA 23681, United States 2 Northrup Grumman Space Technology, 293 Highway 247 South, WRG4, Warner Robins, GA 31088, United States 3 Department of Mathematics and Statistics, Old Dominion University, Norfolk, Virginia 23529-0077, Uruguay 4 Department of Mathematics, Mahidol University, Bangkok, Thailand

Received  April 2006 Revised  January 2007 Published  June 2007

In this paper, we provide an error analysis for the $p$-version of the discontinuous Galerkin finite element method for a class of heat transfer problems in built-up structures. Also, a general form of the matrix associated with the discretization of time variable using the $p$-finite element basis functions is established. Many interesting properties of this matrix are obtained. Numerical examples are provided in the last section.
Citation: Kim S. Bey, Peter Z. Daffer, Hideaki Kaneko, Puntip Toghaw. Error analysis of the p-version discontinuous Galerkin method for heat transfer in built-up structures. Communications on Pure and Applied Analysis, 2007, 6 (3) : 719-740. doi: 10.3934/cpaa.2007.6.719
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