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<p>We investigate a space-time finite element method for solving a parabolic advection-diffusion problem. We use the Banach-Nečas-Babuška theorem to show the well-posedness of the continuous Petrov-Galerkin variational formulation for this problem. A fully discrete finite-element scheme is analyzed using the standard Galerkin method and unstructured meshes. An optimal error estimate is established in a discrete energy norm under a globally regularity condition. Some numerical results corroborate our theoretical results.</p>

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A Priori Error Analysis of a Space-Time Finite Element Method for Advection-Diffusion Equations

  • 期刊论文

  • 发表日期：

    2026年2月23日

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  • Thi Thanh Mai Ta

摘要

We investigate a space-time finite element method for solving a parabolic advection-diffusion problem. We use the Banach-Nečas-Babuška theorem to show the well-posedness of the continuous Petrov-Galerkin variational formulation for this problem. A fully discrete finite-element scheme is analyzed using the standard Galerkin method and unstructured meshes. An optimal error estimate is established in a discrete energy norm under a globally regularity condition. Some numerical results corroborate our theoretical results.