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|Title:||Discontinuous galerkin methods for quasi-linear elliptic problems of nonmonotone type|
|Citation:||SIAM JOURNAL ON NUMERICAL ANALYSIS, 45(1), 163-192|
|Abstract:||In this paper, both symmetric and nonsymmetric interior penalty discontinuous hp-Galerkin methods are applied to a class of quasi-linear elliptic problems which are of nonmonotone type. Using Brouwer's fixed point theorem, it is shown that the discrete problem has a solution, and then, using Lipschitz continuity of the discrete solution map, uniqueness is also proved. A priori error estimates in the broken H-1-norm, which are optimal in h and suboptimal in p, are derived. Moreover, on a regular mesh an hp-error estimate for the L-2-norm is also established. Finally, numerical experiments illustrating the theoretical results are provided.|
|Appears in Collections:||Article|
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