Time discretisation of monotone nonlinear evolution problems by the discontinuous Galerkin method

Abstract

A class of discontinuous Galerkin methods is studied for the time discretisation of the initial-value problem for a nonlinear first-order evolution equation that is governed by a monotone, coercive, and hemicontinuous operator. The numerical solution is shown to converge towards the weak solution of the original problem. Furthermore, well-posedness of the time-discrete problem as well as a priori error estimates for sufficiently smooth exact solutions are studied.

Nonlinear stochastic evolution equations of second order with damping

“…We consider a bounded domain D in R d with smooth boundary and take V A = V B = H 1 0 (D), the standard Sobolev space, and H = L 2 (D). Following Emmrich [7], we consider ρ : R d → R d given by…”

“…, the standard Sobolev space, and H = L 2 (D). Following Emmrich [7], we consider ρ : R d → R d given by…”