Spectral element spatial discretization error in solving highly anisotropic heat conduction equation. This paper describes a study of the effects of the overall spatial resolution, polynomial degree and computational grid directionality on the accuracy of numerical solutions of a highly anisotropic thermal diffusion equation using the spectral element spatial discretization method. The high-order spectral element macroscopic modeling code SEL/HiFi has been used to explore the parameter space. It is shown that for a given number of spatial degrees of freedom, increasing polynomial degree while reducing the number of elements results in exponential reduction of the numerical error. The alignment of the grid with the direction of anisotropy is shown to further improve the accuracy of the solution. These effects are qualitatively explained and numerically quantified in 2- and 3-dimensional calculations with straight and curved anisotropy.

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  1. Araki, Samuel J.; Wirz, Richard E.: Cell-centered particle weighting algorithm for PIC simulations in a non-uniform 2D axisymmetric mesh (2014)
  2. van Es, Bram; Koren, Barry; de Blank, Hugo J.: Finite-difference schemes for anisotropic diffusion (2014)
  3. Jardin, S. C.: Review of implicit methods for the magnetohydrodynamic description of magnetically confined plasmas (2012)
  4. Meier, E. T.; Glasser, A. H.; Lukin, V. S.; Shumlak, U.: Modeling open boundaries in dissipative MHD simulation (2012)
  5. Liseikin, V. D.; Rychkov, A. D.; Kofanov, A. V.: Applications of a comprehensive grid method to solution of three-dimensional boundary value problems (2011)
  6. Lowrie, W.; Lukin, V. S.; Shumlak, U.: A priori mesh quality metric error analysis applied to a high-order finite element method (2011)
  7. Adams, Mark F.; Samtaney, Ravi; Brandt, Achi: Toward textbook multigrid efficiency for fully implicit resistive magnetohydrodynamics (2010)
  8. Meier, E. T.; Lukin, V. S.; Shumlak, U.: Spectral element spatial discretization error in solving highly anisotropic heat conduction equation (2010)
  9. Strauss, H. R.; Hientzsch, B.; Chen, J.: A spectral element implementation for the M3D extended MHD code (2008)
  10. Jardin, S. C.; Breslau, J.; Ferraro, N.: A high-order implicit finite element method for integrating the two-fluid magnetohydrodynamic equations in two dimensions (2007)
  11. Lin, Guang; Karniadakis, George Em: A discontinuous Galerkin method for two-temperature plasmas (2006)
  12. Glasser, A. H.; Tang, X. Z.: The SEL macroscopic modeling code (2004)
  13. Jardin, S. C.: A triangular finite element with first-derivative continuity applied to fusion MHD applications (2004)
  14. Rossmanith, James A.: A high-resolution constrained transport method with adaptive mesh refinement for ideal MHD (2004)