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- W862596102 abstract "with homogenous Dirichlet boundary condition, where ut is the time partial derivative of u(x, t); a(x) is a uniformly positive on Ω and a(x), f(x, t) and u(x) are assumed to be sufficiently smooth. Since the 1950s, scientists have formulated time-stepping procedures to numerically approximate the solutions of such problems. Numerical methods for such parabolic problems can be classified as two categories. The first category consists of finite difference methods that use difference quotient to replace differential quotient and the other refers to as finite element methods, see, e.g., [3, 6, 7, 12–14, 18] and references in. The WG-FEMs, which was first introduced by Wang and Ye [16] for solving the second order elliptic problems, are newly developed FEMs. The novel idea of WG-FEMs is to introduce weak functions and weak derivatives, and allows the use of totally discontinuous piecewise polynomials in the finite element procedure. Later, The WG -FEMs were studied from implementation point of view in [8] and applied to solve the Helmholtz problem with high wave numbers in [10]. A WG-FEM was introduced and analyzed for parabolic equations based on a discrete weak gradient arising from local RT [11]. Due to the use of RT elements, the WG finite element" @default.
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- W862596102 date "2014-06-01" @default.
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- W862596102 title "On L<sup>2</sup> Error Estimate for Weak Galerkin Finite Element Methods for Parabolic Problems" @default.
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- W862596102 doi "https://doi.org/10.4208/jcm.1401-m4385" @default.
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