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An adaptive discontinuous finite volume element method for the Allen-Cahn equation
In this paper, the discontinuous finite volume element method (DFVEM) is considered to solve the Allen-Cahn equation which contains strong...
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An Upwind Mixed Finite Volume Element-fractional Step Method and Convergence Analysis for Three-dimensional Compressible Contamination Treatment from Nuclear Waste
In this paper the authors discuss a numerical simulation problem of three-dimensional compressible contamination treatment from nuclear waste. The...
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A Quadratic Discontinuous Finite Volume Element Scheme for Stokes Problems
In this paper, we construct a quadratic discontinuous finite volume scheme for Stokes equations. Specifically, the quadratic discontinuous finite...
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Space-Time Adaptive ADER-DG Finite Element Method with LST-DG Predictor and a posteriori Sub-cell WENO Finite-Volume Limiting for Simulation of Non-stationary Compressible Multicomponent Reactive Flows
The space-time adaptive ADER finite element DG method with a posteriori correction technique of solutions on subcells by the finite-volume ADER-WENO...
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Mesh Conditions of the Preserving-Maximum-Principle Linear Finite Volume Element Method for Anisotropic Diffusion-Convection-Reaction Equations
We develop mesh conditions for linear finite volume element approximations of anisotropic diffusionconvectionreaction problems to satisfy the...
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Unified construction and L2 analysis for the finite volume element method over tensorial meshes
We provide a unified construction for high order finite volume element (FVE) schemes with the optimal
L 2 convergence rate over tensorial meshes in... -
Introduction to the Finite Element Method
The first chapter classifies the content as well as the focus of this textbook. The importance of computational methods in the modern design process...
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A Mixed Finite Element and Characteristic Mixed Finite Element for Incompressible Miscible Darcy-Forchheimer Displacement and Numerical Analysis
In this paper a mixed finite element-characteristic mixed finite element method is discussed to simulate an incompressible miscible Darcy-Forchheimer...
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The Hermite Finite Volume Method with Global Conservation Law
We construct a high-order (cubic) Hermite finite volume method (FVM-2L) with a two-layered dual strategy on triangular meshes, which possesses the...
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The Finite Element Method
For d = 1, 2, 3, consider the Poisson equation in a bounded d-dimensional domain as a model problem. We describe the basic components of the finite...
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An entropy stable finite volume method for a compressible two phase model
We study a binary mixture of compressible viscous fluids modelled by the Navier-Stokes-Allen-Cahn system with isentropic or ideal gas law. We propose...
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The finite volume element method for the two-dimensional space-fractional convection–diffusion equation
We develop a fully discrete finite volume element scheme of the two-dimensional space-fractional convection–diffusion equation using the finite...
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A structure-preserving finite element method for the multi-phase Mullins–Sekerka problem with triple junctions
We consider a sharp interface formulation for the multi-phase Mullins–Sekerka flow. The flow is characterized by a network of curves evolving such...
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Pointwise adaptive non-conforming finite element method for the obstacle problem
In this article, we develop a posteriori error analysis of a non-conforming finite element method in the supremum norm for the elliptic obstacle...
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A weak Galerkin finite-element method for singularly perturbed convection–diffusion–reaction problems with interface
In this paper, a weak Galerkin (WG) finite-element method is developed and analyzed for singularly perturbed convection–diffusion–reaction problems...
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Two-grid Method of Expanded Mixed Finite Element Approximations for Parabolic Integro-differential Optimal Control Problems
This paper aims to construct a two-grid scheme of fully discretized expanded mixed finite element methods for optimal control problems governed by...
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On the condition number of the finite element method for the Laplace–Beltrami operator
We give an upper bound for the condition number of the finite element operator for the Laplace-Beltrami operator on closed surfaces immersed in
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An Energy-based Overset Finite Element Method for Pseudo-static Structural Analysis
This paper addresses a simple energy-based overset finite element method (EbO-FEM) to solve pseudo-static deformation problems consisting of...
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Solving the Pure Neumann Problem by a Mixed Finite Element Method
AbstractThis paper proposes a new method for the numerical solution of the pure Neumann problem for the diffusion equation in a mixed formulation....
