Optimal Error Estimates for Fully Discrete Galerkin Approximations of Semilinear Parabolic Equations

Abstract

We consider a semilinear parabolic equation with a large class of nonlinearities without any growth conditions. We discretize the problem with a discontinuous Galerkin scheme dG(0) in time (which is a variant of the implicit Euler scheme) and with conforming finite elements in space. The main contribution of this paper is the proof of the uniform boundedness of the discrete solution. This allows us to obtain optimal error estimates with respect to various norms.

References in corpus (1)

• Discrete maximal parabolic regularity for Galerkin finite element methods for non-autonomous parabolic problem s

Cited by in corpus (3)

• On a randomized backward Euler method for nonlinear evolution equations with time-irregular coefficients
• A priori error estimates for the space-time finite element approximation of a non-smooth optimal control problem governed by a coupled semilinear PDE-ODE system
• Weak discrete maximum principle of finite element methods in convex polyhedra