SIAM Journal on Numerical Analysis
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Pseudospectral (PS) methods are widely used for solving partial differential equations (PDEs) to high accuracy in simple geometries. They can be seen as the limit of finite difference methods for i...
1 CitationsSource
#1Huayi WeiH-Index: 7
#2Xuehai HuangH-Index: 1
Last. Ao LiH-Index: 1
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Piecewise divergence-free nonconforming virtual elements are designed for Stokes problem in any dimensions. After introducing a local energy projector based on the Stokes problem and the stabilizat...
1 CitationsSource
Generalized plane waves (GPWs) were introduced to take advantage of Trefftz methods for problems modeled by variable coefficient equations. Despite the fact that GPWs do not satisfy the Trefftz pro...
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A family of arbitrarily high-order fully discrete space-time finite element methods are proposed for the nonlinear Schrodinger equation based on the scalar auxiliary variable formulation, which con...
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Dziuk's surface finite element method (FEM) for mean curvature flow has had a significant impact on the development of parametric and evolving surface FEMs for surface evolution equations and curva...
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We deal with the numerical solution of nonlinear time-dependent convection-diffusion-reaction equations with the aid of continuous and discontinuous Galerkin discretization of an arbitrary polynomi...
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In this manuscript we study the properties of a family of a second-order differential equations with damping, its discretizations, and their connections with accelerated optimization algorithms for...
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Shape gradients have been widely used in numerical shape gradient descent algorithms for shape optimization. The two types of shape gradients, i.e., the distributed one and the boundary type, are e...
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Optimal order error estimates of the energy-preserving numerical methods for solving the Hodge wave equation is obtained in this paper. Based on the de Rham complex, the Hodge wave equation can be ...
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This paper presents a novel mathematical framework for understanding pixel-driven approaches for the parallel beam Radon transform as well as for the fanbeam transform, showing that with the correc...
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Mathematical optimization
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Finite element method
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