Discontinuous Galerkin method for the three-dimensional problem of thermoelasticity

• Autorzy: Węgrzyn-Skrzypczak Ewa

Identyfikatory

DOI

10.17512/jamcm.2019.4.11

• Języki publikacji: EN

Abstrakty

EN

The paper is focused on the mathematical and numerical approaches for the thermoelasticity problem in the three-dimensional domain. The mathematical description of considered problem is based on the second order differential equations of elasticity with the term describing thermal deformations. The numerical model uses the discontinuous Galerkin method which is widely used to solve the problems of hydrodynamics. The presented paper shows the possibility of using the mentioned method to solve the problem of thermomechanics.

Słowa kluczowe

EN

thermoelasticity; finite element method; discontinuous Galerkin method

PL

termoelastyczność; metoda elementów skończonych; nieciągła metoda Galerkina

• Wydawca: Wydawnictwo Politechniki Częstochowskiej
• Czasopismo: Journal of Applied Mathematics and Computational Mechanics
• Rocznik: 2019
• Tom: Vol. 18, nr 4
• Strony: 115--126
• Opis fizyczny: Bibliogr. 9 poz., rys., tab.

Twórcy

autor

Węgrzyn-Skrzypczak Ewa

• Institute of Mathematics, Czestochowa University of Technology Czestochowa, Poland

Bibliografia

• [1] Cockburn, B., Karniadakis, G.E., & Shu, C.W. (2000). Discontinuous Galerkin Methods. Theory, Computations and Applications, vol. 11 of Lecture Notes in Computational Science and Engineering, Berlin: Springer.
• [2] Lew, A., Neff, P., Sulsky, D., & Ortiz, M. (2004). Optimal BV estimates for a discontinuous Galerkin method for linear elasticity. Applied Mathematics Research Express, 3, 73-106.
• [3] Hansbo, P., & Larson, M.G. (2002). Discontinuous Galerkin methods for incompressible and nearly incompressible elasticity by Nitsche’s method. Computer Methods in Applied Mechanics and Engineering, 191(17-18), 1895-1908.
• [4] Hansbo, P., & Larson, M.G. (2003). Discontinuous Galerkin and the Crouzeix-Raviart element: Application to Elasticity. Mathematical Modelling and Numerical Analysis, 37(1), 63-72.
• [5] Riviere, B. (2008). Discontinuous Galerkin methods for solving elliptic and parabolic equations: Theory and implementation. Frontiers in Mathematics 35, SIAM.
• [6] Chen, Y., Huang, J., Huang, X., & Xu Y. (2010). On the local discontinuous Galerkin method for linear elasticity. Mathematical Problems in Engineering, 20.
• [7] Arnold, D.N., & Winther, R. (2002). Mixed finite elements for elasticity. Numerische Mathematik, 92(3), 401-419.
• [8] Adams, S., & Cockburn, B. (2005). A mixed finite element method for elasticity in three dimensions. Journal of Scientific Computing, 25(3), 515-521.
• [9] Li, B.Q. (2006). Discontinuous Finite Elements in Fluid Dynamics and Heat Transfer. London: Springer-Verlag.

Uwagi

Opracowanie rekordu ze środków MNiSW, umowa Nr 461252 w ramach programu "Społeczna odpowiedzialność nauki" - moduł: Popularyzacja nauki i promocja sportu (2020).