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A High-Order Shifted Boundary Virtual Element Method for Poisson Equations on 2D Curved Domains
We consider a high-order virtual element method for Poisson problems with non-homogeneous Dirichlet boundary condition on 2D domains with curved...
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On the finite difference method with penalty for numerical solution of PDEs over curved domains
This paper aims to decipher the elliptic PDEs defined over curved complex domains with a penalty approach in a finite difference scheme. Using the...
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Operator Estimates for Problems in Domains with Singularly Curved Boundary: Dirichlet and Neumann Conditions
AbstractWe consider a system of second-order semilinear elliptic equations in a multidimensional domain with an arbitrarily curved boundary contained...
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Finite Fourier Series in Hyperbolic Initial-Boundary Value Problems for Domains with Curved Boundaries
AbstractThe Fourier method based on orthogonal splines is used to solve a linear hyperbolic initial-boundary value problem for a domain with a curved...
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Hybrid High-Order Methods for Elliptic PDEs on Curved and Complicated Domains
We introduce a variant of the hybrid high-order method (HHO) employing Nitsche’s boundary penalty techniques for the Poisson problem on the curved...
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An Unfitted Finite Element Method by Direct Extension for Elliptic Problems on Domains with Curved Boundaries and Interfaces
We propose and analyze an unfitted finite element method of arbitrary order for solving elliptic problems on domains with curved boundaries and...
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The Nonconforming Virtual Element Method with Curved Edges
We introduce a nonconforming virtual element method for the Poisson problem on domains with fixed curved boundary and internal interfaces. We prove...
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A New Approach to Handle Curved Meshes in the Hybrid High-Order Method
We present here a novel approach to handling curved meshes in polytopal methods within the framework of hybrid high-order methods. The hybrid...
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Nonpositively Curved Surfaces are Loewner
We show that every closed nonpositively curved surface satisfies Loewner’s systolic inequality. The proof relies on a combination of the Gauss–Bonnet...
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Operator Estimates for Planar Domains with Irregularly Curved Boundary. The Dirichlet and Neumann Conditions
We consider a general nonselfadjoint second order scalar operator in a planar domain such that one of the boundary components is obtained by an...
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Solving Elliptic PDE’s Using Polynomial Splines on Curved Triangulations
It is shown how the polynomial splines defined on the curved triangulations introduced in our recent paper Larry L. Schumaker, A. Yu. (Comput. Aided...
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Accurate High-Order Tensor-Product Generalized Summation-By-Parts Discretizations of Hyperbolic Conservation Laws: General Curved Domains and Functional Superconvergence
The goal of this paper is to outline the requirements for obtaining accurate solutions and functionals from high-order tensor-product generalized...
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On the Equilibrium of Elastic Bodies with a Weakly Curved Junction
AbstractThe paper addresses the analysis of a boundary value problem with an unknown contact area that describes equilibrium of two-dimensional...
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The Unfitted HHO Method for the Stokes Problem on Curved Domains
We design a hybrid high-order (HHO) method to approximate the Stokes problem on curved domains using unfitted meshes. We prove inf-sup stability and...
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Intrinsic Ultracontractivity for Domains in Negatively Curved Manifolds
Let M be a complete, non-compact, connected Riemannian manifold with Ricci curvature bounded from below by a negative constant. A sufficient...
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High-Order Method with Moving Frames to Compute the Covariant Derivatives of Vectors on General 2D Curved Surfaces
The covariant derivative is a generalization of differentiating vectors. The Euclidean derivative is a special case of the covariant derivative in...
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Uniform Decay Rates for a Variable-Coefficient Structural Acoustic Model with Curved Interface on a Shallow Shell
Uniform stabilization of a structural acoustic model describing an acoustic chamber with flexible curved wall is addressed. The coupled nonlinear...
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A Nonnested Augmented Subspace Method for Elliptic Eigenvalue Problems with Curved Interfaces
In this paper, we present a nonnested augmented subspace algorithm and its multilevel correction method for solving elliptic eigenvalue problems with...
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Spectral convergence of Neumann Laplacian perturbed by an infinite set of curved holes
We propose the novel spectral properties of the Neumann Laplacian in a two-dimensional bounded domain perturbed by an infinite number of compact sets...
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Spectral Laplace Transform of Signals on Arbitrary Domains
The Laplace transform is a central mathematical tool for analysing 1D/2D signals and for the solution to PDEs; however, its definition and...
