Work

Fully discrete pointwise smoothing error estimates for measure valued initial data

Year: 2023

Type: article

Abstract: In this paper we analyze a homogeneous parabolic problem with initial data in the space of regular Borel measures. The problem is discretized in time with a discontinuous Galerkin scheme of arbitrary degree and in space with continuous finite elements of orders one or two. We show parabolic smoothing results for the continuous, semidiscrete and fully discrete problems. Our main results are interior L∞ error estimates for the evaluation at the endtime, in cases where the initial data is supported in a subdomain. In order to obtain these, we additionally show interior L∞ error estimates for L2 initial data and quadratic finite elements, which extends the corresponding result previously established by the authors for linear finite elements.

Source: ESAIM Mathematical Modelling and Numerical Analysis

DOI: 10.1051/m2an/2023076

Authors: Dmitriy Leykekhman, Boris Vexler, Jakob Wagner

Institutions: University of Connecticut, Technical University of Munich

Language: English

Topic: Advanced Numerical Methods in Computational Mathematics

Subfield: Computational Mechanics

Field: Engineering

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid:

OpenAlex ID: W4367191002