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In this paper, we carry out the numerical analysis of a class of quasilinear parabolic equations, where the diffusion coefficient depends on the solution of the partial differential equation. The… Click to show full abstract
In this paper, we carry out the numerical analysis of a class of quasilinear parabolic equations, where the diffusion coefficient depends on the solution of the partial differential equation. The goal is to prove error estimates for the fully discrete equation using discontinuous Galerkin discretization in time DG(0) combined with piecewise linear finite elements in space. This analysis is performed under minimal regularity assumptions on the data. In particular, we omit any assumption regarding existence of a second derivative in time of the solution.
Journal Title: Numerische Mathematik
Year Published: 2019
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