Abstract
The purpose of this paper is to provide an error analysis for the p-version of the discontinuous Galerkin finite element method for heat transfer in built-up structures. As a special case of the results in this paper, a theoretical error estimate for the numerical experiments recently conducted by James Tomey is obtained.
Highlights
The purposes of this paper are to report the state of the art information on the time discretization techniques in the discontinuous Galerkin method for parabolic problems and to establish an error analysis for the p-version of the finite element method for such problems (Section 2)
A general form of the matrix which results from the discretization of time variable using p-finite element basis functions is presented
We extend the discussion in [12] by exhibiting the general form for Aand state its characteristics
Summary
The purposes of this paper are to report the state of the art information on the time discretization techniques in the discontinuous Galerkin method for parabolic problems (this section) and to establish an error analysis for the p-version of the finite element method for such problems (Section 2). The current method avoids the complex number arithmetic, and since we are dealing with real data in applications, it may be more appropriate for numerical computations The advantage of this choice as basis elements in time variable lies in the formations of tn tn−1. Formula (3.8) provides a general construction method for the assembly of the pfinite element matrix with any order p when the Legendre polynomials are used in time variable. We observed that the real Schur decomposition approach works well in our numerical experiments It is more of a theoretical interest that we present some observations we obtained concerning the characteristics of the matrix Aand the possibility of it being diagonalized. A proof of this conjecture would settle the question of the diagonalization of An
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