Core Concepts
Proving error bounds for POD-ROM approximations of time-dependent PDEs.
Abstract
This paper analyzes the discretization of time-dependent partial differential equations using POD-ROM methods. It focuses on continuous-in-time approximations, error bounds, and snapshot-based methods. The study includes semilinear reaction-diffusion problems and optimal error estimates. Numerical studies support the analysis.
Introduction:
Study on discretization of time-dependent PDEs using POD-ROM methods.
Proper Orthogonal Decomposition:
Describes two approaches: finite differences with respect to time and time derivatives case.
Preliminaries and Notation:
Standard notation for Sobolev spaces and norms.
Preliminary Results:
Lemmas providing bounds for Galerkin approximations in space.
Error Analysis of the Method:
Semi-discrete POD-ROM approximation for solving PDEs with error bounds analysis.
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