Numerical Methods for Partial Differential Equations最新文献_第8页

Spatio‐temporal scalar auxiliary variable approach for the nonlinear convection–diffusion equation with discontinuous Galerkin method 用不连续Galerkin方法求解非线性对流扩散方程的时空标量辅助变量法

IF 3.9 3区数学

Numerical Methods for Partial Differential Equations Pub Date : 2023-07-19 DOI: 10.1002/num.23061

Yaping Li, W. Zhao, Wenju Zhao

{"title":"Spatio‐temporal scalar auxiliary variable approach for the nonlinear convection–diffusion equation with discontinuous Galerkin method","authors":"Yaping Li, W. Zhao, Wenju Zhao","doi":"10.1002/num.23061","DOIUrl":"https://doi.org/10.1002/num.23061","url":null,"abstract":"In this paper, a scalar auxiliary variable approach combining with a discontinuous Galerkin method is proposed to handle the gradient‐type nonlinear term. The nonlinear convection–diffusion equation is used as the model. The proposed equivalent system can effectively handle the nonlinear convection term by incorporating the spatial and temporal information, globally. With the introduced auxiliary variable, the stability of the system can be simply characterized. In the space, according to the regularity of the system, an optimal accuracy is obtained with the discontinuous Galerkin method. Two different time discretization techniques, that is, backward Euler and linearly extrapolated Crank–Nicolson schemes, are separately considered with first order and second order accuracy. The proposed schemes are unconditionally stable with proper selected parameters. For the error estimates, the optimal convergence rates are rigorously proved. In the numerical experiments, the convergence information is confirmed and a benchmark problem with shock tendency is then followed with robustness demonstration.","PeriodicalId":19443,"journal":{"name":"Numerical Methods for Partial Differential Equations","volume":" ","pages":""},"PeriodicalIF":3.9,"publicationDate":"2023-07-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48751612","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Superconvergence analysis of the bilinear‐constant scheme for two‐dimensional incompressible convective Brinkman–Forchheimer equations 二维不可压缩对流Brinkman-Forchheimer方程双线性常数格式的超收敛分析

IF 3.9 3区数学

Numerical Methods for Partial Differential Equations Pub Date : 2023-07-18 DOI: 10.1002/num.23060

Huaijun Yang, Xu Jia

引用次数: 0

Two‐sided Krylov enhanced proper orthogonal decomposition methods for partial differential equations with variable coefficients 变系数偏微分方程的双侧Krylov增强的正正交分解方法

IF 3.9 3区数学

Numerical Methods for Partial Differential Equations Pub Date : 2023-07-05 DOI: 10.1002/num.23058

Li Wang, Zhen Miao, Yaolin Jiang

{"title":"Two‐sided Krylov enhanced proper orthogonal decomposition methods for partial differential equations with variable coefficients","authors":"Li Wang, Zhen Miao, Yaolin Jiang","doi":"10.1002/num.23058","DOIUrl":"https://doi.org/10.1002/num.23058","url":null,"abstract":"In this paper, new fast computing methods for partial differential equations with variable coefficients are studied and analyzed. They are two kinds of two‐sided Krylov enhanced proper orthogonal decomposition (KPOD) methods. First, the spatial discrete scheme of an advection‐diffusion equation is obtained by Galerkin approximation. Then, an algorithm based on a two‐sided KPOD approach involving the block Arnoldi and block Lanczos processes for the obtained time‐varying equations is put forward. Moreover, another type of two‐sided KPOD algorithm based on Laguerre orthogonal polynomials in frequency domain is provided. For the two kinds of two‐sided KPOD methods, we present a theoretical analysis for the moment matching of the discrete time‐invariant transfer function in time domain and give the error bound caused by the reduced‐order projection between the Galerkin finite element solution and the approximate solution of the two‐sided KPOD method. Finally, the feasibility of four two‐sided KPOD algorithms is verified by several numerical results with different inputs and setting parameters.","PeriodicalId":19443,"journal":{"name":"Numerical Methods for Partial Differential Equations","volume":" ","pages":""},"PeriodicalIF":3.9,"publicationDate":"2023-07-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47673516","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Issue Information 问题信息

IF 3.9 3区数学

Numerical Methods for Partial Differential Equations Pub Date : 2023-07-05 DOI: 10.1002/num.22891

引用次数: 0

A priori error estimates of two monolithic schemes for Biot's consolidation model Biot固结模型两个整体方案的先验误差估计

IF 3.9 3区数学

Numerical Methods for Partial Differential Equations Pub Date : 2023-06-29 DOI: 10.1002/num.23059

H. Gu, M. Cai, Jingzhi Li, Guoliang Ju

引用次数: 1

Neilan's divergence‐free finite elements for Stokes equations on tetrahedral grids 四面体网格上Stokes方程的Neilan无发散有限元

IF 3.9 3区数学

Numerical Methods for Partial Differential Equations Pub Date : 2023-06-28 DOI: 10.1002/num.23055

Shangyou Zhang

引用次数: 1

Conservative EQ1rot nonconforming FEM for nonlinear Schrödinger equation with wave operator 带波动算子的非线性Schrödinger方程的保守EQ1rot非协调有限元

IF 3.9 3区数学

Numerical Methods for Partial Differential Equations Pub Date : 2023-06-26 DOI: 10.1002/num.23057

Lingli Wang, Mike Meng-Yen Li, S. Peng

{"title":"Conservative EQ1rot nonconforming FEM for nonlinear Schrödinger equation with wave operator","authors":"Lingli Wang, Mike Meng-Yen Li, S. Peng","doi":"10.1002/num.23057","DOIUrl":"https://doi.org/10.1002/num.23057","url":null,"abstract":"In this paper, we consider leap‐frog finite element methods with EQ1rot$$ {mathrm{EQ}}_1^{mathrm{rot}} $$ element for the nonlinear Schrödinger equation with wave operator. We propose that both the continuous and discrete systems can keep mass and energy conservation. In addition, we focus on the unconditional superconvergence analysis of the numerical scheme, the key of which is the time‐space error splitting technique. The spatial error is derived τ$$ tau $$ independently with order O(h2+hτ)$$ Oleft({h}^2+ htau right) $$ in H1$$ {H}^1 $$ ‐norm, where h$$ h $$ and τ$$ tau $$ denote the space and time step size. Then the unconditional optimal L2$$ {L}^2 $$ error and superclose result with order O(h2+τ2)$$ Oleft({h}^2+{tau}^2right) $$ are deduced, and the unconditional optimal H1$$ {H}^1 $$ error is obtained with order O(h+τ2)$$ Oleft(h+{tau}^2right) $$ by using interpolation theory. The final unconditional superconvergence result with order O(h2+τ2)$$ Oleft({h}^2+{tau}^2right) $$ is derived by the interpolation postprocessing technique. Furthermore, we apply the proposed leap‐frog finite element methods to solve the logarithmic Schrödinger equation with wave operator by introducing a regularized system with a small regularization parameter 0","PeriodicalId":19443,"journal":{"name":"Numerical Methods for Partial Differential Equations","volume":"1 1","pages":""},"PeriodicalIF":3.9,"publicationDate":"2023-06-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42545899","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

An efficient and accurate numerical method for the fractional optimal control problems with fractional Laplacian and state constraint 具有分数阶拉普拉斯算子和状态约束的分数阶最优控制问题的一种有效而精确的数值方法

IF 3.9 3区数学

Numerical Methods for Partial Differential Equations Pub Date : 2023-06-26 DOI: 10.1002/num.23056

Jiaqi Zhang, Y. Yang

引用次数: 0

Optimal convergence rate of the explicit Euler method for convection–diffusion equations II: High dimensional cases 对流扩散方程的显式欧拉法的最优收敛速率II:高维情况

3区数学

Numerical Methods for Partial Differential Equations Pub Date : 2023-06-26 DOI: 10.1002/num.23054

Qifeng Zhang, Jiyuan Zhang, Zhi‐zhong Sun

{"title":"Optimal convergence rate of the explicit Euler method for convection–diffusion equations II: High dimensional cases","authors":"Qifeng Zhang, Jiyuan Zhang, Zhi‐zhong Sun","doi":"10.1002/num.23054","DOIUrl":"https://doi.org/10.1002/num.23054","url":null,"abstract":"Abstract This is the second part of study on the optimal convergence rate of the explicit Euler discretization in time for the convection–diffusion equations [Zhang et al. Appl. Math. Lett. 131 (2022), 108048] which focuses on high‐dimensional linear/nonlinear cases under Dirichlet/Neumann boundary conditions. Several new difference schemes are proposed based on the explicit Euler discretization in temporal derivative and centered difference discretization in spatial derivatives. The priori estimate of the improved difference scheme with application to the constant convection coefficients is performed under the maximum norm and the optimal convergence rate four is achieved when the step‐ratios along each direction equal to . Also we give partial results for the three‐dimensional case. The improved difference schemes have essentially improved the CFL condition and the numerical accuracy comparing with the classical difference schemes. Numerical examples involving two‐/three‐dimensional linear/nonlinear problems under Dirichlet/Neumann boundary conditions such as the Fisher equation, the Chafee–Infante equation and the Burgers' equation substantiate the good properties claimed for the improved difference scheme.","PeriodicalId":19443,"journal":{"name":"Numerical Methods for Partial Differential Equations","volume":"14 3 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-06-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135608808","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 1

A new high order hybrid WENO scheme for hyperbolic conservation laws 双曲守恒律的一种新的高阶混合WENO格式

IF 3.9 3区数学

Numerical Methods for Partial Differential Equations Pub Date : 2023-06-19 DOI: 10.1002/num.23052

Liang Li, Zhenming Wang, Zhonglong Zhao, Jun Zhu

{"title":"A new high order hybrid WENO scheme for hyperbolic conservation laws","authors":"Liang Li, Zhenming Wang, Zhonglong Zhao, Jun Zhu","doi":"10.1002/num.23052","DOIUrl":"https://doi.org/10.1002/num.23052","url":null,"abstract":"This article proposes an improved hybrid weighted essentially non‐oscillatory (WENO) scheme based on the third‐ and fifth‐order finite‐difference modified WENO (MWENO) schemes developed by Zhu et al. in (SIAM J. Sci. Comput. 39 (2017), A1089–A1113.) for solving hyperbolic conservation laws. The MWENO schemes give a guideline on whether to use the WENO scheme or the linear upwind scheme. Unfortunately, because there is no explicit formula for computing the roots of algebraic polynomials of order four or higher, it is difficult to generalize this criterion to higher order cases. Therefore, this article proposes a simple criterion for constructing a series of seventh‐, ninth‐, and higher‐order hybrid WENO schemes, and then designs a class of improved smooth indicator WENO (WENO‐MS) schemes. Compared with the classical WENO schemes, the main advantages of the WENO‐MS schemes are their robustness and efficiency. And these WENO‐MS schemes are more efficient, have better resolution, and can solve many extreme problems without any additional techniques. Furthermore, a simplification criterion is proposed to further improve the computational efficiency of the WENO‐MS schemes, and these simple WENO‐MS schemes are abbreviated as WENO‐SMS schemes in this article. Extensive numerical results demonstrate the good performance of the WENO‐MS schemes and the WENO‐SMS schemes.","PeriodicalId":19443,"journal":{"name":"Numerical Methods for Partial Differential Equations","volume":"39 1","pages":"4347 - 4376"},"PeriodicalIF":3.9,"publicationDate":"2023-06-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48895129","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0