Interior Penalty Discontinuous Galerkin Methods with Implicit Time-integration Techniques for Nonlinear Parabolic Equations
نویسندگان
چکیده
We prove existence and numerical stability of numerical solutions of three fully discrete interior penalty discontinuous Galerkin (IPDG) methods for solving nonlinear parabolic equations. Under some appropriate regularity conditions, we give the l(H) and l(L) error estimates of the fully discrete symmetric interior penalty discontinuous Galerkin (SIPG) 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. key words. discontinuous Galerkin method; error estimate; existence; numerical stability; nonlinear parabolic equation
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