Optimal error estimates for linear parabolic problems under minimal regularity assumptions
The paper deals with error estimates connected with the discretization of a linear parabolic problem \(u_ t+Au=f, u(x,0)=0\) on \(\Omega\), \(u(x,t)=0\) on \(\partial \Omega \times(0,\infty)\) via Galerkin approximation in space and \(\theta\)-method (\(\theta\geq frac{1}{2})\) in time. The error is evaluated in norms of the type \(H_ t^{\delta}(H^ 1_ x)\cap H_ t^{\delta +1/2}(L^ 2_ x)\) for \(| \delta | \leq 1/2\). The derived error estimates are optimal with respect to regularity assumptions on the right-hand side f.
scientific article; zbMATH DE number 3856349