We study the convergence and error estimates of a finite volume method for the compressible Navier-Stokes-Fourier system with Dirichlet boundary conditions. Physical fluid domain is typically smooth and needs to be approximated by a polygonal computational domain. This leads to domain-related discretization errors, the so-called variational crimes. To treat them efficiently we embed the fluid domain into a large enough cubed domain, and propose a finite volume scheme for the corresponding domain-penalized problem. Under the assumption that the numerical density and temperature are uniformly bounded, we derive the ballistic energy inequality, yielding a priori estimates and the consistency of the penalization finite volume approximations. Further, we show that the numerical solutions converge weakly to a generalized, the so-called dissipative measure-valued, solution of the corresponding Dirichlet problem. If a strong solution exists, we prove that our numerical approximations converge strongly with the rate 1/4. Additionally, assuming uniform boundedness of the approximate velocities, we obtain global existence of the strong solution. In this case we prove that the numerical solutions converge strongly to the strong solution with the optimal rate 1/2.
Enabling fast convergence of the iterated penalty Picard iteration with $O(1)$ penalty parameter for incompressible Navier-Stokes via Anderson acceleration
Pressure and convection robust bounds for continuous interior penalty divergence-free finite element methods for the incompressible Navier-Stokes equations
On $C^{0}$ Interior Penalty Method for Fourth Order Dirichlet Boundary Control Problem and a New Error Analysis for Fourth Order Elliptic Equation with Cahn-Hilliard Boundary Condition
Stability estimates of Nyström discretizations of Helmholtz decomposition boundary integral equation formulations for the solution of Navier scattering problems in two dimensions with Dirichlet boundary conditions
Penalty-Free Natural Deep Ritz Method Based on de Rham Complex for High-Dimensional Dirichlet Boundary Value Problems
School of Mathematics and Statistics, Beijing Institute of Technology（北京理工大学数学与统计学院）；Beijing Key Laboratory on MCAACI, Beijing Institute of Technology（北京理工大学MCAACI北京市重点实验室）；Institute of Computational Mathematics and Scientific/Engineering Computing, Academy of Mathematics and Systems Science, Chinese Academy of Sciences（中国科学院数学与系统科学研究院计算数学与科学工程计算研究所）；University of Chinese Academy of Sciences（中国科学院大学）
RBFs methods for null control problems of the Stokes system with Dirichlet and Navier slip boundary conditions
Instituto de Matemáticas, Universidad Nacional Autónoma de México（墨西哥国立自治大学数学研究所）；Departamento de Matemática, Universidad Técnica Federico Santa María（智利弗雷德里科·圣玛丽亚理工大学数学系）
Parallel Nodal Interior-Penalty Discontinuous Galerkin Methods for the Subsonic Compressible Navier-Stokes Equations: Applications to Vortical Flows and VIV Problems
Convergence of a Vector Penalty Projection Scheme for the Navier-Stokes Equations with moving body
Université de Bordeaux, IMB, CNRS UMR5251（波尔多大学，IMB）；Bordeaux INP, Institut de Mathématiques de Bordeaux, CNRS UMR5251, ENSEIRB-MATMECA（波尔多国立理工学院，波尔多数学研究所）
The Penalty Cell-Centered Finite Element Scheme For Stokes Problem On General Meshes
Faculty of Mathematics and Computer Science, University of Science, VNU HCMC（越南国立大学胡志明市科技大学数学与计算机科学系）；Faculty of Mathematics-Informatics, Ho Chi Minh City University of Pedagogy（胡志明市师范大学生物信息学系）
A Nitsche method for Navier--Stokes/generalized poroelasticity interface problems
Indian Institute of Technology Roorkee（印度理工学院鲁尔基分校）；Pontificia Universidad Católica de Chile（智利天主教公立大学）；Centro de Modelamiento Matemático (CNRS IRL2807)（数学建模中心（法国国家科学研究中心国际研究联络处2807））；Monash University（蒙纳士大学）；Universidad Adventista de Chile（智利基督复临安息日会大学）
Convergence of a finite volume method to weak solutions for the compressible Navier-Stokes-Fourier system
Institute of Mathematics of the Academy of Sciences of the Czech Republic（捷克科学院数学研究所）；Institute of Mathematics, Johannes Gutenberg-University Mainz（约翰内斯·古腾堡美因茨大学数学研究所）；Academy for Multidisciplinary studies, Capital Normal University（首都师范大学多学科研究院）；School of Mathematics, Nanjing University of Aeronautics and Astronautics（南京航空航天大学数学学院）
