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Keywords:

  • discontinuous Galerkin method;
  • error estimate;
  • existence;
  • numerical stability;
  • nonlinear parabolic equation

Abstract

We prove existence and numerical stability of numerical solutions of three fully discrete interior penalty discontinuous Galerkin methods for solving nonlinear parabolic equations. Under some appropriate regularity conditions, we give the l2(H1) and l(L2) error estimates of the fully discrete symmetric interior penalty discontinuous Galerkin–scheme with the implicit θ -schemes in time, which include backward Euler and Crank–Nicolson finite difference approximations. Our estimates are optimal with respect to the mesh size h. The theoretical results are confirmed by some numerical experiments. © 2012 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2013