This paper considers weak Galerkin finite element approximations on polygonal/polyhedral meshes for a quasistatic Maxwell viscoelastic model.The spatial discretization uses piecewise polynomials of degree k(k≥1)for t...This paper considers weak Galerkin finite element approximations on polygonal/polyhedral meshes for a quasistatic Maxwell viscoelastic model.The spatial discretization uses piecewise polynomials of degree k(k≥1)for the stress approximation,degree k+1 for the velocity approximation,and degree k for the numerical trace of velocity on the inter-element boundaries.The temporal discretization in the fully discrete method adopts a backward Euler difference scheme.We show the existence and uniqueness of the semi-discrete and fully discrete solutions,and derive optimal a priori error estimates.Numerical examples are provided to support the theoretical analysis.展开更多
We study the asymptotic-preserving fully discrete schemes for nonequilibrium radiation diffusion problem in spherical and cylindrical symmetric geometry.The research is based on two-temperature models with Larsen’s f...We study the asymptotic-preserving fully discrete schemes for nonequilibrium radiation diffusion problem in spherical and cylindrical symmetric geometry.The research is based on two-temperature models with Larsen’s flux-limited diffusion operators.Finite volume spatially discrete schemes are developed to circumvent the singularity at the origin and the polar axis and assure local conservation.Asymmetric second order accurate spatial approximation is utilized instead of the traditional first order one for boundary flux-limiters to consummate the schemes with higher order global consistency errors.The harmonic average approach in spherical geometry is analyzed,and its second order accuracy is demonstrated.By formal analysis,we prove these schemes and their corresponding fully discrete schemes with implicitly balanced and linearly implicit time evolutions have first order asymptoticpreserving properties.By designing associated manufactured solutions and reference solutions,we verify the desired performance of the fully discrete schemes with numerical tests,which illustrates quantitatively they are first order asymptotic-preserving and basically second order accurate,hence competent for simulations of both equilibrium and non-equilibrium radiation diffusion problems.展开更多
Weak Galerkin finite element method is introduced for solving wave equation with interface on weak Galerkin finite element space(Pk(K),P_(k−1)(∂K),[P_(k−1)(K)]^(2)).Optimal order a priori error estimates for both spac...Weak Galerkin finite element method is introduced for solving wave equation with interface on weak Galerkin finite element space(Pk(K),P_(k−1)(∂K),[P_(k−1)(K)]^(2)).Optimal order a priori error estimates for both space-discrete scheme and implicit fully discrete scheme are derived in L1(L2)norm.This method uses totally discontinuous functions in approximation space and allows the usage of finite element partitions consisting of general polygonal meshes.Finite element algorithm presented here can contribute to a variety of hyperbolic problems where physical domain consists of heterogeneous media.展开更多
基金This work was supported by the National Natural Science Foundation of China(Grant No.12171340).
文摘This paper considers weak Galerkin finite element approximations on polygonal/polyhedral meshes for a quasistatic Maxwell viscoelastic model.The spatial discretization uses piecewise polynomials of degree k(k≥1)for the stress approximation,degree k+1 for the velocity approximation,and degree k for the numerical trace of velocity on the inter-element boundaries.The temporal discretization in the fully discrete method adopts a backward Euler difference scheme.We show the existence and uniqueness of the semi-discrete and fully discrete solutions,and derive optimal a priori error estimates.Numerical examples are provided to support the theoretical analysis.
基金The authors are very grateful to the editors and the anonymous referees for helpful suggestions to enhance the paper.This work is supported by the National Natural Science Foundation of China(11271054,11471048,11571048,U1630249)the Science Foundation of CAEP(2014A0202010)the Science Challenge Project(No.JCKY2016212A502)and the Foundation of LCP.
文摘We study the asymptotic-preserving fully discrete schemes for nonequilibrium radiation diffusion problem in spherical and cylindrical symmetric geometry.The research is based on two-temperature models with Larsen’s flux-limited diffusion operators.Finite volume spatially discrete schemes are developed to circumvent the singularity at the origin and the polar axis and assure local conservation.Asymmetric second order accurate spatial approximation is utilized instead of the traditional first order one for boundary flux-limiters to consummate the schemes with higher order global consistency errors.The harmonic average approach in spherical geometry is analyzed,and its second order accuracy is demonstrated.By formal analysis,we prove these schemes and their corresponding fully discrete schemes with implicitly balanced and linearly implicit time evolutions have first order asymptoticpreserving properties.By designing associated manufactured solutions and reference solutions,we verify the desired performance of the fully discrete schemes with numerical tests,which illustrates quantitatively they are first order asymptotic-preserving and basically second order accurate,hence competent for simulations of both equilibrium and non-equilibrium radiation diffusion problems.
文摘Weak Galerkin finite element method is introduced for solving wave equation with interface on weak Galerkin finite element space(Pk(K),P_(k−1)(∂K),[P_(k−1)(K)]^(2)).Optimal order a priori error estimates for both space-discrete scheme and implicit fully discrete scheme are derived in L1(L2)norm.This method uses totally discontinuous functions in approximation space and allows the usage of finite element partitions consisting of general polygonal meshes.Finite element algorithm presented here can contribute to a variety of hyperbolic problems where physical domain consists of heterogeneous media.
