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arXiv · 2412.08375

Error analysis for discontinuous Galerkin time-stepping methods for nonlinear parabolic equations via maximal regularity

Georgios Akrivis·Stig Larsson
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Abstract

We consider the discretization of a class of nonlinear parabolic equations by discontinuous Galerkin time-stepping methods and establish a priori as well as conditional a posteriori error estimates. Our approach is motivated by the error analysis in [9] for Runge-Kutta methods for nonlinear parabolic equations; in analogy to [9], the proofs are based on maximal regularity properties of discontinuous Galerkin methods for non-autonomous linear parabolic equations.

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Georgios Akrivis, Stig Larsson. 2024-12-11. Error analysis for discontinuous Galerkin time-stepping methods for nonlinear parabolic equations via maximal regularity. https://arxiv.org/abs/2412.08375

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